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Important questions for class 10 maths chapter 12 areas related to circles with solutions

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The document contains important questions and solutions for Class 10 Mathematics, specifically focused on Chapter 12: Areas Related to Circles. It includes short answer and long answer type questions regarding the area of shaded regions involving squares, semicircles, and circles, offering detailed solutions to help students prepare for their exams. The document is structured to enhance understanding and scoring in board examinations.

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Expert’s class Ahmedabad Dhruv Thakar 8320495706 1 Important Questions for Class 10 Maths Chapter 12 Areas Related to Circles With Solutions 2016 Short Answer Type Questions II [3 Marks] Question 1. In figure, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square as diameter. Find the area of the shaded region. Solution: Area of the square ABCD = 14 x 14 = 196 cm² Area of semicircle AOB=1/2 x πr² =1/2×22/7x7x7 Similarly, area of semicircle DOC = 77 cm² Hence, the area of shaded region (Part W and Part Y) = Area of square -Area of two semicircles AOB and COD = 196 – 154 = 42 cm² Therefore, area of four shaded parts (i.e. X, Y, W, Z) = (2 x 42) cm² = 84 cm² Question 2. In figure, are shown two arcs PAQ and PBQ. Arc PAQ is a part of circle with centre O and radius OP while arc PBQ is a semicircle drawn on PQ as diameter with centre M. If OP = PQ = 10 cm, show that area of shaded region is 25(√3- π /6)cm² Solution: OP = OQ = 10 cm
Expert’s class Ahmedabad Dhruv Thakar 8320495706 2 PQ = 10 cm So, ΔOPQ is an equilateral triangle ∠POQ = 60° Area of segment PAQM = Area of sector OPAQ – Area of ΔOPQ =60/360 x π x 10 x 10-√3/4 x 10 x 10 =(100π/6-100√3/4)cm² Area of semicircle =1/2 x π x 5 x 5 = 25/2π cm² Area of the shaded region =25/2π-(100π/6-100√3/4)=25π/2-50π/3+25√3 =75π-100π/6+25√3=25√3-25π/6 =25(√3-π/6)cm² Question 3. In figure, O is the centre of a circle such that diameter AB = 13 cm and AC = 12 cm. BC is joined. Find the area of the shaded region. Solution: Here, BC² = AB²-AC² = 169-144 = 25 BC = 5 Area of shaded region = Area of semicircle – Area of right triangle ABC =1/2 x πr²-1/2AC x BC =1/2 x 3.14(13/2)²-1/2 x 12 x 5 =66.33 – 30 = 36.33 cm² Question 4. In figure, find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where∠AOC = 40°. Solution: Area of shaded region=360°-θ/360° x π(R²-r²) =320°/360° x π[(14)²-(7)²] =8/9 x 22/7(196-49)=8/9 x 22/7 x 147 =1232/3=410.67 cm² Question 5. Find the area of shaded region in figure, where a circle of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm
Expert’s class Ahmedabad Dhruv Thakar 8320495706 3 Solution: Area of ΔOAB=√3/4(side)²=√3/4 x (12)² =36√3=36 x 1.73 =62.28 cm² area of circle with center O =πr²=3.14 x (6)² =3.14 x 36 =113.04 cm² area of sector(OLQP)=πr² x θ/360°=3.14 x 6² x 60°/360° =3.14 x 36 x 1/6 =18.84 cm² area of shaded region=area of ΔOAB+area of circle-2 area of sector OLQP =(62.28+113.04-2 x 18.84)cm² =137.64cm² Question 6. In figure, is a chord AB of a circle, with centre O and radius 10 cm, that subtends a right angle at the centre of the circle. Find the area of the minor segment AQBP. Hence, find the area of major segment ALBQA Solution: Area of minor segment APBQ=θ/360° x πr²-r²sin45°cos45° =3.14 x 100/4-100 x 1/√2 x 1/√2 =(78.5-50)cm²=28.5 cm² Area of major segment ALBQA =πr²-area of minor segment =3.14 x (10)²-28.5 =(314-28.5)cm²=285.5 cm² Long Answer Type Questions [4 Marks] Question 7. An elastic belt is placed around the rim of a pulley of radius 5 cm. From one point C on the belt, the elastic belt is pulled directly away from the centre O of the pulley until it is at P, 10 cm from the point O. Find the length of the belt that is still in contact with the pulley.Also find the shaded area, (use π = 3.14
Expert’s class Ahmedabad Dhruv Thakar 8320495706 4 and √3 = 1.73) Solution:
Expert’s class Ahmedabad Dhruv Thakar 8320495706 5 Question 8. In figure, is shown a sector OAP of a circle with centre O, containing Z0. AB is perpendicular to the radius OA and meets OP produced at B. Prove that the perimeter of shaded region is r[tanθ+secθ+πθ/180-1]
Expert’s class Ahmedabad Dhruv Thakar 8320495706 6 Solution: Question 9. Find the area of the shaded region in figure, where APD, AQB, BRC and CSD are semi-circles of diameter 14 cm, 3.5 cm, 7 cm and 3.5 cm respectively Solution: Area of shaded region = Area of semicircle APD + Area of semicircle BRC – 2 x Area of semicircle AQB
Expert’s class Ahmedabad Dhruv Thakar 8320495706 7 2015 Short Answer Type Questions II [3 Marks Question 10. In figure, APB and AQO are semicircle, and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region. Solution: Let r be the radius of the semicircle APB, i.e. OB = OA = r, then r/2 is the radius of the semicircle AQO.
Expert’s class Ahmedabad Dhruv Thakar 8320495706 8 Question 11. In figure, find the area of the shaded region Solution: Question 12. Find the area of the minor segment of a circle of radius 14 cm, when its central angle is 60°. Also find the area of the corresponding major segment Solution: Question 13. All the vertices of a rhombus lie on a circle.Find the area of rhombus,if the area of circle is 1256 cm²
Expert’s class Ahmedabad Dhruv Thakar 8320495706 9 Solution: Question 14. The long and short hand of a clock are 6cm and 4 cm long respectively,Find the sum of the distance travelled by their tips in 24hrs. Solution: Question 15. Solution:
Expert’s class Ahmedabad Dhruv Thakar 8320495706 10 Long Answer Type Questions [4 Marks] Question 16. In Figure, PQRS is a square lawn with side PQ = 42 metres. Two circular flower beds are there on the sides PS and QR with centre at O, the intersection of its diagonals. Find the total area of the two flower beds (shaded parts). Solution:
Expert’s class Ahmedabad Dhruv Thakar 8320495706 11 2014 Short Answer Type Questions I [2 Marks] Question 17. In figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region Solution:
Expert’s class Ahmedabad Dhruv Thakar 8320495706 12 Question 18. In figure, OABC is a quadrant of a circle of radius 7 cm. If OD = 4 cm, find the area of the shaded region Solution: Short Answer Type Questions II [3 Marks] Question 19. In figure, a circle is inscribed in an equilateral triangle ABC of side 12 cm. Find the radius of inscribed circle and the area of the shaded region
Expert’s class Ahmedabad Dhruv Thakar 8320495706 13 Solution: Question 20. In figure, PSR, RTQ and PAQ are three semicircles of diameters 10 cm, 3 cm and 7 cm respectively. Find the perimeter of the shaded region Solution:
Expert’s class Ahmedabad Dhruv Thakar 8320495706 14 Question 21. In figure, two concentric circles with centre O, have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region Solution: Question 22. In figure, ABCD is a trapezium of area 24.5 sq. cm. In it, AD ¦ ¦ BC, ∠DAB = 90°, AD = 10 cm and BC = 4 cm. If ABE is a quadrant of a circle, find the area of the shaded region
Expert’s class Ahmedabad Dhruv Thakar 8320495706 15 Solution: Question 23. In figure, ABDC is a quadrant of a circle of radius 28 cm and a semicircle BEC is drawn with BC as diameter. Find B the area of the shaded region. Solution:
Expert’s class Ahmedabad Dhruv Thakar 8320495706 16 2013 Short Answer Type Questions I [2 Marks] Question 24. Two circular pieces of equal radii and maximum area,touching each other are cut out from a rectangular cardboard of dimensions 14 cm x 7 cm. Find the area of the remaining cardboard Solution: Question 25. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes. Solution: Question 26. In the given figure,the area of the shaded region between two concentric circles is 286 cm2.If the difference of the radii of the two circles is 7 cm, find the sum of their radii.
Expert’s class Ahmedabad Dhruv Thakar 8320495706 17 Solution: Short Answer Type Questions II [3 Marks] Question 27. In the given figure AB and CD are two diameters of a circle with centre O,Which are perpendicular to each other.OB is the diameter of small circle.If OA=7cm,find area of shaded region Solution: Question 28. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find 1. the length of the arc 2. area of the sector formed by the arc.
Expert’s class Ahmedabad Dhruv Thakar 8320495706 18 Solution: Question 29. In figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 21 cm, find the area of the shaded region Solution: Question 30. A chord of length 10 cm divides a circle of radius 5√2 cm in two segments. Find the area of the minor segment Solution:
Expert’s class Ahmedabad Dhruv Thakar 8320495706 19 Question 31. In the given figure, from each corner of a square of side 4 cm, a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut. Find the area of the shaded region. Solution: 2012 Short Answer Type Questions I [2 Marks]
Expert’s class Ahmedabad Dhruv Thakar 8320495706 20 Question 32. In figure, OABC is a square of side 7cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region Solution: Question 33. In figure, ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of the shaded region Solution: Refer to Ans 31. Question 34. From a rectangular sheet of paper ABCD with AB = 40 cm and AD = 28 cm, semicircular portion with BC as diameter is cut off. Find the area of the remaining paper. Solution:
Expert’s class Ahmedabad Dhruv Thakar 8320495706 21 Question 35. In the given figure, the shape of the top of a table is that a sector of a circle with centre O and ∠AOB = 90°. If AO = OB = 42 cm,then find the perimeter of the top of the table Solution: Short Answer Type Questions II [3 Marks] Question 36. In figure, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and 3.5 cm and centre O. If ∠POQ = 30°, then find the area of the shaded region. Solution: Question 37. In figure, find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC are semicircles.
Expert’s class Ahmedabad Dhruv Thakar 8320495706 22 Solution: Question 38. In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region. Solution: Question 39. Find the area of the shaded region in Figure, if ABCD is a square of side 28 cm and APD and BPC are semicircles.
Expert’s class Ahmedabad Dhruv Thakar 8320495706 23 Solution: Question 40. In figure, ABCD is a square of side 7 cm. DPBA and DQBC are quadrants of circles, each of radius 7 cm. Find the area of the shaded region. Solution: side of square=7cm
Expert’s class Ahmedabad Dhruv Thakar 8320495706 24 radius of circle=7cm Areas Related to Circles Chapter Wise Important Questions Class 10 Mathematics August 20, 2018 by Fazal 1 Comment Important Questions for Class 10 Maths Chapter 12 Areas Related to Circles with solutions includes all the important topics with detailed explanation that aims to help students to score more marks in Board Exams 2020. Students who are preparing for their Class 10 exams must go through Important Questions for Class 10 Math Chapter 12 Areas Related to Circles. Important Questions for Class 10 Maths Chapter 12 Areas Related to Circles With Solutions Expert teachers at CBSETuts.com collected and solved 2 Marks and 4 mark important questions for Class 10 Maths Chapter 12 Areas Related to Circles. MathsScienceEnglishSocialHindi AHindi B 2016 Short Answer Type Questions II [3 Marks] Question 1. In figure, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square as diameter. Find the area of the shaded region.
Expert’s class Ahmedabad Dhruv Thakar 8320495706 25 Solution: Area of the square ABCD = 14 x 14 = 196 cm² Area of semicircle AOB=1/2 x πr² =1/2×22/7x7x7 Similarly, area of semicircle DOC = 77 cm² Hence, the area of shaded region (Part W and Part Y) = Area of square -Area of two semicircles AOB and COD = 196 – 154 = 42 cm² Therefore, area of four shaded parts (i.e. X, Y, W, Z) = (2 x 42) cm² = 84 cm² Question 2. In figure, are shown two arcs PAQ and PBQ. Arc PAQ is a part of circle with centre O and radius OP while arc PBQ is a semicircle drawn on PQ as diameter with centre M. If OP = PQ = 10 cm, show that area of shaded region is 25(√3- π /6)cm² Solution: OP = OQ = 10 cm PQ = 10 cm So, ΔOPQ is an equilateral triangle ∠POQ = 60° Area of segment PAQM = Area of sector OPAQ – Area of ΔOPQ =60/360 x π x 10 x 10-√3/4 x 10 x 10 =(100π/6-100√3/4)cm² Area of semicircle =1/2 x π x 5 x 5 = 25/2π cm² Area of the shaded region =25/2π-(100π/6-100√3/4)=25π/2-50π/3+25√3 =75π-100π/6+25√3=25√3-25π/6 =25(√3-π/6)cm² Question 3. In figure, O is the centre of a circle such that diameter AB = 13 cm and AC =
Expert’s class Ahmedabad Dhruv Thakar 8320495706 26 12 cm. BC is joined. Find the area of the shaded region. Solution: Here, BC² = AB²-AC² = 169-144 = 25 BC = 5 Area of shaded region = Area of semicircle – Area of right triangle ABC =1/2 x πr²-1/2AC x BC =1/2 x 3.14(13/2)²-1/2 x 12 x 5 =66.33 – 30 = 36.33 cm² Question 4. In figure, find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where∠AOC = 40°. Solution: Area of shaded region=360°-θ/360° x π(R²-r²) =320°/360° x π[(14)²-(7)²] =8/9 x 22/7(196-49)=8/9 x 22/7 x 147 =1232/3=410.67 cm² Question 5. Find the area of shaded region in figure, where a circle of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm Solution: Area of ΔOAB=√3/4(side)²=√3/4 x (12)² =36√3=36 x 1.73 =62.28 cm² area of circle with center O =πr²=3.14 x (6)² =3.14 x 36 =113.04 cm²
Expert’s class Ahmedabad Dhruv Thakar 8320495706 27 area of sector(OLQP)=πr² x θ/360°=3.14 x 6² x 60°/360° =3.14 x 36 x 1/6 =18.84 cm² area of shaded region=area of ΔOAB+area of circle-2 area of sector OLQP =(62.28+113.04-2 x 18.84)cm² =137.64cm² Question 6. In figure, is a chord AB of a circle, with centre O and radius 10 cm, that subtends a right angle at the centre of the circle. Find the area of the minor segment AQBP. Hence, find the area of major segment ALBQA Solution: Area of minor segment APBQ=θ/360° x πr²-r²sin45°cos45° =3.14 x 100/4-100 x 1/√2 x 1/√2 =(78.5-50)cm²=28.5 cm² Area of major segment ALBQA =πr²-area of minor segment =3.14 x (10)²-28.5 =(314-28.5)cm²=285.5 cm² Long Answer Type Questions [4 Marks] Question 7. An elastic belt is placed around the rim of a pulley of radius 5 cm. From one point C on the belt, the elastic belt is pulled directly away from the centre O of the pulley until it is at P, 10 cm from the point O. Find the length of the belt that is still in contact with the pulley.Also find the shaded area, (use π = 3.14 and √3 = 1.73) Solution:
Expert’s class Ahmedabad Dhruv Thakar 8320495706 28
Expert’s class Ahmedabad Dhruv Thakar 8320495706 29 Question 8. In figure, is shown a sector OAP of a circle with centre O, containing Z0. AB is perpendicular to the radius OA and meets OP produced at B. Prove that the perimeter of shaded region is r[tanθ+secθ+πθ/180-1] Solution: Question 9. Find the area of the shaded region in figure, where APD, AQB, BRC and CSD are semi-circles of diameter 14 cm, 3.5 cm, 7 cm and 3.5 cm respectively Solution: Area of shaded region = Area of semicircle APD + Area of semicircle BRC – 2 x Area of semicircle AQB
Expert’s class Ahmedabad Dhruv Thakar 8320495706 30 2015 Short Answer Type Questions II [3 Marks Question 10. In figure, APB and AQO are semicircle, and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region. Solution: Let r be the radius of the semicircle APB, i.e. OB = OA = r, then r/2 is the radius of the semicircle AQO.
Expert’s class Ahmedabad Dhruv Thakar 8320495706 31 Question 11. In figure, find the area of the shaded region Solution: Question 12. Find the area of the minor segment of a circle of radius 14 cm, when its central angle is 60°. Also find the area of the corresponding major segment Solution: Question 13. All the vertices of a rhombus lie on a circle.Find the area of rhombus,if the area of circle is 1256 cm²
Expert’s class Ahmedabad Dhruv Thakar 8320495706 32 Solution: Question 14. The long and short hand of a clock are 6cm and 4 cm long respectively,Find the sum of the distance travelled by their tips in 24hrs. Solution: Question 15. Solution:
Expert’s class Ahmedabad Dhruv Thakar 8320495706 33 Long Answer Type Questions [4 Marks] Question 16. In Figure, PQRS is a square lawn with side PQ = 42 metres. Two circular flower beds are there on the sides PS and QR with centre at O, the intersection of its diagonals. Find the total area of the two flower beds (shaded parts). Solution:
Expert’s class Ahmedabad Dhruv Thakar 8320495706 34 2014 Short Answer Type Questions I [2 Marks] Question 17. In figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region Solution:
Expert’s class Ahmedabad Dhruv Thakar 8320495706 35 Question 18. In figure, OABC is a quadrant of a circle of radius 7 cm. If OD = 4 cm, find the area of the shaded region Solution: Short Answer Type Questions II [3 Marks] Question 19. In figure, a circle is inscribed in an equilateral triangle ABC of side 12 cm. Find the radius of inscribed circle and the area of the shaded region
Expert’s class Ahmedabad Dhruv Thakar 8320495706 36 Solution: Question 20. In figure, PSR, RTQ and PAQ are three semicircles of diameters 10 cm, 3 cm and 7 cm respectively. Find the perimeter of the shaded region Solution:
Expert’s class Ahmedabad Dhruv Thakar 8320495706 37 Question 21. In figure, two concentric circles with centre O, have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region Solution: Question 22. In figure, ABCD is a trapezium of area 24.5 sq. cm. In it, AD ¦ ¦ BC, ∠DAB = 90°, AD = 10 cm and BC = 4 cm. If ABE is a quadrant of a circle, find the area of the shaded region
Expert’s class Ahmedabad Dhruv Thakar 8320495706 38 Solution: Question 23. In figure, ABDC is a quadrant of a circle of radius 28 cm and a semicircle BEC is drawn with BC as diameter. Find B the area of the shaded region. Solution:
Expert’s class Ahmedabad Dhruv Thakar 8320495706 39 2013 Short Answer Type Questions I [2 Marks] Question 24. Two circular pieces of equal radii and maximum area,touching each other are cut out from a rectangular cardboard of dimensions 14 cm x 7 cm. Find the area of the remaining cardboard Solution: Question 25. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes. Solution: Question 26. In the given figure,the area of the shaded region between two concentric circles is 286 cm2.If the difference of the radii of the two circles is 7 cm, find the sum of their radii.
Expert’s class Ahmedabad Dhruv Thakar 8320495706 40 Solution: Short Answer Type Questions II [3 Marks] Question 27. In the given figure AB and CD are two diameters of a circle with centre O,Which are perpendicular to each other.OB is the diameter of small circle.If OA=7cm,find area of shaded region Solution: Question 28. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find 1. the length of the arc 2. area of the sector formed by the arc.
Expert’s class Ahmedabad Dhruv Thakar 8320495706 41 Solution: Question 29. In figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 21 cm, find the area of the shaded region Solution: Question 30. A chord of length 10 cm divides a circle of radius 5√2 cm in two segments. Find the area of the minor segment Solution:
Expert’s class Ahmedabad Dhruv Thakar 8320495706 42 Question 31. In the given figure, from each corner of a square of side 4 cm, a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut. Find the area of the shaded region. Solution: 2012 Short Answer Type Questions I [2 Marks]
Expert’s class Ahmedabad Dhruv Thakar 8320495706 43 Question 32. In figure, OABC is a square of side 7cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region Solution: Question 33. In figure, ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of the shaded region Solution: Refer to Ans 31. Question 34. From a rectangular sheet of paper ABCD with AB = 40 cm and AD = 28 cm, semicircular portion with BC as diameter is cut off. Find the area of the remaining paper. Solution:
Expert’s class Ahmedabad Dhruv Thakar 8320495706 44 Question 35. In the given figure, the shape of the top of a table is that a sector of a circle with centre O and ∠AOB = 90°. If AO = OB = 42 cm,then find the perimeter of the top of the table Solution: Short Answer Type Questions II [3 Marks] Question 36. In figure, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and 3.5 cm and centre O. If ∠POQ = 30°, then find the area of the shaded region. Solution: Question 37. In figure, find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC are semicircles.
Expert’s class Ahmedabad Dhruv Thakar 8320495706 45 Solution: Question 38. In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region. Solution: Question 39. Find the area of the shaded region in Figure, if ABCD is a square of side 28 cm and APD and BPC are semicircles.
Expert’s class Ahmedabad Dhruv Thakar 8320495706 46 Solution: Question 40. In figure, ABCD is a square of side 7 cm. DPBA and DQBC are quadrants of circles, each of radius 7 cm. Find the area of the shaded region. Solution: side of square=7cm radius of circle=7cm
Expert’s class Ahmedabad Dhruv Thakar 8320495706 47 Question 41. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 10 minutes Solution: 2011 Short Answer Type Questions I [2 Marks] Question 42. In figure APB and CQD are semicircles of diameter 7 cm each, while ARC and BSD are semicircles of diameter 14 cm each. Find the perimeter of the shaded region
Expert’s class Ahmedabad Dhruv Thakar 8320495706 48 Solution: Question 43. Find the area of a quadrant of a circle, where the circumference of circle is 44cm Solution: Question 44. Find the perimeter of the shaded region in figure, if ABCD is a square of side 14 cm and APB and CPD are semicircles
Expert’s class Ahmedabad Dhruv Thakar 8320495706 49 Solution: Question 45. In given figure, a semicircle is drawn with O as centre and AB as diameter. Semicircles are drawn with AO and OB as diameters.If AB = 28 m, find the perimeter of the shaded region Solution: Question 46. In given figure, ABC is a triangle right-angled atB, with AB = 14 cm and BC = 24 cm. With thevertices A, B and C as centres, arcs are drawn each of radius 7 cm. Find the area of the shaded region.
Expert’s class Ahmedabad Dhruv Thakar 8320495706 50 Solution: Question 47. In the given figure, OABC is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region Solution: Short Answer Type Questions II [3 Marks] Question 48. Find the area of the major segment APB in figure of a circle of radius 35 cm and ∠AOB = 90°.
Expert’s class Ahmedabad Dhruv Thakar 8320495706 51 Solution: Question 49. A chord of a circle of radius 14 cm subtends an angle of 120° at the centre. Find the area of the corresponding minor segment of the circle. Solution: Question 50. A chord of a circle of radius 21 cm subtends an angle of 60° at the centre. Find the area of the corresponding minor segment of the circle
Expert’s class Ahmedabad Dhruv Thakar 8320495706 52 Solution: Question 51. Area of a sector of a circle of radius 14 cm is 154 cm². Find the length of the corresponding arc of the sector Solution: Question 52. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding minor segment and hence find the area of the major segment
Expert’s class Ahmedabad Dhruv Thakar 8320495706 53 Solution: Long Answer Type Questions [4 Marks] Question 53. In figure, arcs are drawn by taking vertices A, B and C of an equilateral triangle ABC of side 14 cm as centres to intersect the sides BC, CA and AB at their respective mid-point D, E and E Find the area of the shaded region Solution: Question 54. The length and breadth of a rectangular piece of paper are 28 cm and 14 cm respectively. A semi-circular portion is cut off from the breadth’s side and a semicircular portion is added on length’s side, as shown in figure. Find the area of shaded region
Expert’s class Ahmedabad Dhruv Thakar 8320495706 54 Solution: Question 55. Find the area of shaded region in figure,where arcs drawn with centres A,B,C and D intersects at mid point P,Q,R and S of sides AB,BC,CD and DA of a square ABCD,where the length of each side of square is 14 cm Solution: Question 56. In the given figure, three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area of shaded region
Expert’s class Ahmedabad Dhruv Thakar 8320495706 55 enclosed between these three circles Solution: Question 57. In given figure, an equilateral triangle has been inscribed in a circle of radius 6 cm. Find the area of the shaded region. Solution:
Expert’s class Ahmedabad Dhruv Thakar 8320495706 56 Question 58. Find the area of the shaded region in given figure, where ABCD is a square of side 28 cm Solution: Question 59. From a thin metallic piece, in the shape of a trapezium ABCD in which AB ¦¦ CD and ∠BCD = 90°, a quarter circle BFEC is removed (See figure). Given AB = BC = 3.5 cm and DE = 2 cm, calculate the area of the remaining (shaded) part of the metal sheet.
Expert’s class Ahmedabad Dhruv Thakar 8320495706 57 Solution: 2010 Short Answer Type Questions II [3 Marks] Question 60. In figure, the boundary of shaded region consists of four semicircular arcs, two smallest being equal. If diameter of the largest is 14 cm and that of the smallest is 3.5 cm, calculate the area of the shaded region.
Expert’s class Ahmedabad Dhruv Thakar 8320495706 58 Solution: Question 61. Find the area of the shaded region in figure, if AC = 24 cm, BC = 10 cm and O is the centre of the circle Solution: Question 62. In figure, AB and CD are two perpendicular diameters of a circle with centre
Expert’s class Ahmedabad Dhruv Thakar 8320495706 59 O. If OA = 7 cm, find the area of the shaded region Solution: Question 63. Find the area of the shaded region in figure, where a circular arc of radius 7 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm, as centre Solution:
Expert’s class Ahmedabad Dhruv Thakar 8320495706 60

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Important questions for class 10 maths chapter 12 areas related to circles with solutions

  • 1. Expert’s class Ahmedabad Dhruv Thakar 8320495706 1 Important Questions for Class 10 Maths Chapter 12 Areas Related to Circles With Solutions 2016 Short Answer Type Questions II [3 Marks] Question 1. In figure, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square as diameter. Find the area of the shaded region. Solution: Area of the square ABCD = 14 x 14 = 196 cm² Area of semicircle AOB=1/2 x πr² =1/2×22/7x7x7 Similarly, area of semicircle DOC = 77 cm² Hence, the area of shaded region (Part W and Part Y) = Area of square -Area of two semicircles AOB and COD = 196 – 154 = 42 cm² Therefore, area of four shaded parts (i.e. X, Y, W, Z) = (2 x 42) cm² = 84 cm² Question 2. In figure, are shown two arcs PAQ and PBQ. Arc PAQ is a part of circle with centre O and radius OP while arc PBQ is a semicircle drawn on PQ as diameter with centre M. If OP = PQ = 10 cm, show that area of shaded region is 25(√3- π /6)cm² Solution: OP = OQ = 10 cm
  • 2. Expert’s class Ahmedabad Dhruv Thakar 8320495706 2 PQ = 10 cm So, ΔOPQ is an equilateral triangle ∠POQ = 60° Area of segment PAQM = Area of sector OPAQ – Area of ΔOPQ =60/360 x π x 10 x 10-√3/4 x 10 x 10 =(100π/6-100√3/4)cm² Area of semicircle =1/2 x π x 5 x 5 = 25/2π cm² Area of the shaded region =25/2π-(100π/6-100√3/4)=25π/2-50π/3+25√3 =75π-100π/6+25√3=25√3-25π/6 =25(√3-π/6)cm² Question 3. In figure, O is the centre of a circle such that diameter AB = 13 cm and AC = 12 cm. BC is joined. Find the area of the shaded region. Solution: Here, BC² = AB²-AC² = 169-144 = 25 BC = 5 Area of shaded region = Area of semicircle – Area of right triangle ABC =1/2 x πr²-1/2AC x BC =1/2 x 3.14(13/2)²-1/2 x 12 x 5 =66.33 – 30 = 36.33 cm² Question 4. In figure, find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where∠AOC = 40°. Solution: Area of shaded region=360°-θ/360° x π(R²-r²) =320°/360° x π[(14)²-(7)²] =8/9 x 22/7(196-49)=8/9 x 22/7 x 147 =1232/3=410.67 cm² Question 5. Find the area of shaded region in figure, where a circle of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm
  • 3. Expert’s class Ahmedabad Dhruv Thakar 8320495706 3 Solution: Area of ΔOAB=√3/4(side)²=√3/4 x (12)² =36√3=36 x 1.73 =62.28 cm² area of circle with center O =πr²=3.14 x (6)² =3.14 x 36 =113.04 cm² area of sector(OLQP)=πr² x θ/360°=3.14 x 6² x 60°/360° =3.14 x 36 x 1/6 =18.84 cm² area of shaded region=area of ΔOAB+area of circle-2 area of sector OLQP =(62.28+113.04-2 x 18.84)cm² =137.64cm² Question 6. In figure, is a chord AB of a circle, with centre O and radius 10 cm, that subtends a right angle at the centre of the circle. Find the area of the minor segment AQBP. Hence, find the area of major segment ALBQA Solution: Area of minor segment APBQ=θ/360° x πr²-r²sin45°cos45° =3.14 x 100/4-100 x 1/√2 x 1/√2 =(78.5-50)cm²=28.5 cm² Area of major segment ALBQA =πr²-area of minor segment =3.14 x (10)²-28.5 =(314-28.5)cm²=285.5 cm² Long Answer Type Questions [4 Marks] Question 7. An elastic belt is placed around the rim of a pulley of radius 5 cm. From one point C on the belt, the elastic belt is pulled directly away from the centre O of the pulley until it is at P, 10 cm from the point O. Find the length of the belt that is still in contact with the pulley.Also find the shaded area, (use π = 3.14
  • 4. Expert’s class Ahmedabad Dhruv Thakar 8320495706 4 and √3 = 1.73) Solution:
  • 5. Expert’s class Ahmedabad Dhruv Thakar 8320495706 5 Question 8. In figure, is shown a sector OAP of a circle with centre O, containing Z0. AB is perpendicular to the radius OA and meets OP produced at B. Prove that the perimeter of shaded region is r[tanθ+secθ+πθ/180-1]
  • 6. Expert’s class Ahmedabad Dhruv Thakar 8320495706 6 Solution: Question 9. Find the area of the shaded region in figure, where APD, AQB, BRC and CSD are semi-circles of diameter 14 cm, 3.5 cm, 7 cm and 3.5 cm respectively Solution: Area of shaded region = Area of semicircle APD + Area of semicircle BRC – 2 x Area of semicircle AQB
  • 7. Expert’s class Ahmedabad Dhruv Thakar 8320495706 7 2015 Short Answer Type Questions II [3 Marks Question 10. In figure, APB and AQO are semicircle, and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region. Solution: Let r be the radius of the semicircle APB, i.e. OB = OA = r, then r/2 is the radius of the semicircle AQO.
  • 8. Expert’s class Ahmedabad Dhruv Thakar 8320495706 8 Question 11. In figure, find the area of the shaded region Solution: Question 12. Find the area of the minor segment of a circle of radius 14 cm, when its central angle is 60°. Also find the area of the corresponding major segment Solution: Question 13. All the vertices of a rhombus lie on a circle.Find the area of rhombus,if the area of circle is 1256 cm²
  • 9. Expert’s class Ahmedabad Dhruv Thakar 8320495706 9 Solution: Question 14. The long and short hand of a clock are 6cm and 4 cm long respectively,Find the sum of the distance travelled by their tips in 24hrs. Solution: Question 15. Solution:
  • 10. Expert’s class Ahmedabad Dhruv Thakar 8320495706 10 Long Answer Type Questions [4 Marks] Question 16. In Figure, PQRS is a square lawn with side PQ = 42 metres. Two circular flower beds are there on the sides PS and QR with centre at O, the intersection of its diagonals. Find the total area of the two flower beds (shaded parts). Solution:
  • 11. Expert’s class Ahmedabad Dhruv Thakar 8320495706 11 2014 Short Answer Type Questions I [2 Marks] Question 17. In figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region Solution:
  • 12. Expert’s class Ahmedabad Dhruv Thakar 8320495706 12 Question 18. In figure, OABC is a quadrant of a circle of radius 7 cm. If OD = 4 cm, find the area of the shaded region Solution: Short Answer Type Questions II [3 Marks] Question 19. In figure, a circle is inscribed in an equilateral triangle ABC of side 12 cm. Find the radius of inscribed circle and the area of the shaded region
  • 13. Expert’s class Ahmedabad Dhruv Thakar 8320495706 13 Solution: Question 20. In figure, PSR, RTQ and PAQ are three semicircles of diameters 10 cm, 3 cm and 7 cm respectively. Find the perimeter of the shaded region Solution:
  • 14. Expert’s class Ahmedabad Dhruv Thakar 8320495706 14 Question 21. In figure, two concentric circles with centre O, have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region Solution: Question 22. In figure, ABCD is a trapezium of area 24.5 sq. cm. In it, AD ¦ ¦ BC, ∠DAB = 90°, AD = 10 cm and BC = 4 cm. If ABE is a quadrant of a circle, find the area of the shaded region
  • 15. Expert’s class Ahmedabad Dhruv Thakar 8320495706 15 Solution: Question 23. In figure, ABDC is a quadrant of a circle of radius 28 cm and a semicircle BEC is drawn with BC as diameter. Find B the area of the shaded region. Solution:
  • 16. Expert’s class Ahmedabad Dhruv Thakar 8320495706 16 2013 Short Answer Type Questions I [2 Marks] Question 24. Two circular pieces of equal radii and maximum area,touching each other are cut out from a rectangular cardboard of dimensions 14 cm x 7 cm. Find the area of the remaining cardboard Solution: Question 25. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes. Solution: Question 26. In the given figure,the area of the shaded region between two concentric circles is 286 cm2.If the difference of the radii of the two circles is 7 cm, find the sum of their radii.
  • 17. Expert’s class Ahmedabad Dhruv Thakar 8320495706 17 Solution: Short Answer Type Questions II [3 Marks] Question 27. In the given figure AB and CD are two diameters of a circle with centre O,Which are perpendicular to each other.OB is the diameter of small circle.If OA=7cm,find area of shaded region Solution: Question 28. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find 1. the length of the arc 2. area of the sector formed by the arc.
  • 18. Expert’s class Ahmedabad Dhruv Thakar 8320495706 18 Solution: Question 29. In figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 21 cm, find the area of the shaded region Solution: Question 30. A chord of length 10 cm divides a circle of radius 5√2 cm in two segments. Find the area of the minor segment Solution:
  • 19. Expert’s class Ahmedabad Dhruv Thakar 8320495706 19 Question 31. In the given figure, from each corner of a square of side 4 cm, a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut. Find the area of the shaded region. Solution: 2012 Short Answer Type Questions I [2 Marks]
  • 20. Expert’s class Ahmedabad Dhruv Thakar 8320495706 20 Question 32. In figure, OABC is a square of side 7cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region Solution: Question 33. In figure, ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of the shaded region Solution: Refer to Ans 31. Question 34. From a rectangular sheet of paper ABCD with AB = 40 cm and AD = 28 cm, semicircular portion with BC as diameter is cut off. Find the area of the remaining paper. Solution:
  • 21. Expert’s class Ahmedabad Dhruv Thakar 8320495706 21 Question 35. In the given figure, the shape of the top of a table is that a sector of a circle with centre O and ∠AOB = 90°. If AO = OB = 42 cm,then find the perimeter of the top of the table Solution: Short Answer Type Questions II [3 Marks] Question 36. In figure, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and 3.5 cm and centre O. If ∠POQ = 30°, then find the area of the shaded region. Solution: Question 37. In figure, find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC are semicircles.
  • 22. Expert’s class Ahmedabad Dhruv Thakar 8320495706 22 Solution: Question 38. In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region. Solution: Question 39. Find the area of the shaded region in Figure, if ABCD is a square of side 28 cm and APD and BPC are semicircles.
  • 23. Expert’s class Ahmedabad Dhruv Thakar 8320495706 23 Solution: Question 40. In figure, ABCD is a square of side 7 cm. DPBA and DQBC are quadrants of circles, each of radius 7 cm. Find the area of the shaded region. Solution: side of square=7cm
  • 24. Expert’s class Ahmedabad Dhruv Thakar 8320495706 24 radius of circle=7cm Areas Related to Circles Chapter Wise Important Questions Class 10 Mathematics August 20, 2018 by Fazal 1 Comment Important Questions for Class 10 Maths Chapter 12 Areas Related to Circles with solutions includes all the important topics with detailed explanation that aims to help students to score more marks in Board Exams 2020. Students who are preparing for their Class 10 exams must go through Important Questions for Class 10 Math Chapter 12 Areas Related to Circles. Important Questions for Class 10 Maths Chapter 12 Areas Related to Circles With Solutions Expert teachers at CBSETuts.com collected and solved 2 Marks and 4 mark important questions for Class 10 Maths Chapter 12 Areas Related to Circles. MathsScienceEnglishSocialHindi AHindi B 2016 Short Answer Type Questions II [3 Marks] Question 1. In figure, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square as diameter. Find the area of the shaded region.
  • 25. Expert’s class Ahmedabad Dhruv Thakar 8320495706 25 Solution: Area of the square ABCD = 14 x 14 = 196 cm² Area of semicircle AOB=1/2 x πr² =1/2×22/7x7x7 Similarly, area of semicircle DOC = 77 cm² Hence, the area of shaded region (Part W and Part Y) = Area of square -Area of two semicircles AOB and COD = 196 – 154 = 42 cm² Therefore, area of four shaded parts (i.e. X, Y, W, Z) = (2 x 42) cm² = 84 cm² Question 2. In figure, are shown two arcs PAQ and PBQ. Arc PAQ is a part of circle with centre O and radius OP while arc PBQ is a semicircle drawn on PQ as diameter with centre M. If OP = PQ = 10 cm, show that area of shaded region is 25(√3- π /6)cm² Solution: OP = OQ = 10 cm PQ = 10 cm So, ΔOPQ is an equilateral triangle ∠POQ = 60° Area of segment PAQM = Area of sector OPAQ – Area of ΔOPQ =60/360 x π x 10 x 10-√3/4 x 10 x 10 =(100π/6-100√3/4)cm² Area of semicircle =1/2 x π x 5 x 5 = 25/2π cm² Area of the shaded region =25/2π-(100π/6-100√3/4)=25π/2-50π/3+25√3 =75π-100π/6+25√3=25√3-25π/6 =25(√3-π/6)cm² Question 3. In figure, O is the centre of a circle such that diameter AB = 13 cm and AC =
  • 26. Expert’s class Ahmedabad Dhruv Thakar 8320495706 26 12 cm. BC is joined. Find the area of the shaded region. Solution: Here, BC² = AB²-AC² = 169-144 = 25 BC = 5 Area of shaded region = Area of semicircle – Area of right triangle ABC =1/2 x πr²-1/2AC x BC =1/2 x 3.14(13/2)²-1/2 x 12 x 5 =66.33 – 30 = 36.33 cm² Question 4. In figure, find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where∠AOC = 40°. Solution: Area of shaded region=360°-θ/360° x π(R²-r²) =320°/360° x π[(14)²-(7)²] =8/9 x 22/7(196-49)=8/9 x 22/7 x 147 =1232/3=410.67 cm² Question 5. Find the area of shaded region in figure, where a circle of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm Solution: Area of ΔOAB=√3/4(side)²=√3/4 x (12)² =36√3=36 x 1.73 =62.28 cm² area of circle with center O =πr²=3.14 x (6)² =3.14 x 36 =113.04 cm²
  • 27. Expert’s class Ahmedabad Dhruv Thakar 8320495706 27 area of sector(OLQP)=πr² x θ/360°=3.14 x 6² x 60°/360° =3.14 x 36 x 1/6 =18.84 cm² area of shaded region=area of ΔOAB+area of circle-2 area of sector OLQP =(62.28+113.04-2 x 18.84)cm² =137.64cm² Question 6. In figure, is a chord AB of a circle, with centre O and radius 10 cm, that subtends a right angle at the centre of the circle. Find the area of the minor segment AQBP. Hence, find the area of major segment ALBQA Solution: Area of minor segment APBQ=θ/360° x πr²-r²sin45°cos45° =3.14 x 100/4-100 x 1/√2 x 1/√2 =(78.5-50)cm²=28.5 cm² Area of major segment ALBQA =πr²-area of minor segment =3.14 x (10)²-28.5 =(314-28.5)cm²=285.5 cm² Long Answer Type Questions [4 Marks] Question 7. An elastic belt is placed around the rim of a pulley of radius 5 cm. From one point C on the belt, the elastic belt is pulled directly away from the centre O of the pulley until it is at P, 10 cm from the point O. Find the length of the belt that is still in contact with the pulley.Also find the shaded area, (use π = 3.14 and √3 = 1.73) Solution:
  • 28. Expert’s class Ahmedabad Dhruv Thakar 8320495706 28
  • 29. Expert’s class Ahmedabad Dhruv Thakar 8320495706 29 Question 8. In figure, is shown a sector OAP of a circle with centre O, containing Z0. AB is perpendicular to the radius OA and meets OP produced at B. Prove that the perimeter of shaded region is r[tanθ+secθ+πθ/180-1] Solution: Question 9. Find the area of the shaded region in figure, where APD, AQB, BRC and CSD are semi-circles of diameter 14 cm, 3.5 cm, 7 cm and 3.5 cm respectively Solution: Area of shaded region = Area of semicircle APD + Area of semicircle BRC – 2 x Area of semicircle AQB
  • 30. Expert’s class Ahmedabad Dhruv Thakar 8320495706 30 2015 Short Answer Type Questions II [3 Marks Question 10. In figure, APB and AQO are semicircle, and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region. Solution: Let r be the radius of the semicircle APB, i.e. OB = OA = r, then r/2 is the radius of the semicircle AQO.
  • 31. Expert’s class Ahmedabad Dhruv Thakar 8320495706 31 Question 11. In figure, find the area of the shaded region Solution: Question 12. Find the area of the minor segment of a circle of radius 14 cm, when its central angle is 60°. Also find the area of the corresponding major segment Solution: Question 13. All the vertices of a rhombus lie on a circle.Find the area of rhombus,if the area of circle is 1256 cm²
  • 32. Expert’s class Ahmedabad Dhruv Thakar 8320495706 32 Solution: Question 14. The long and short hand of a clock are 6cm and 4 cm long respectively,Find the sum of the distance travelled by their tips in 24hrs. Solution: Question 15. Solution:
  • 33. Expert’s class Ahmedabad Dhruv Thakar 8320495706 33 Long Answer Type Questions [4 Marks] Question 16. In Figure, PQRS is a square lawn with side PQ = 42 metres. Two circular flower beds are there on the sides PS and QR with centre at O, the intersection of its diagonals. Find the total area of the two flower beds (shaded parts). Solution:
  • 34. Expert’s class Ahmedabad Dhruv Thakar 8320495706 34 2014 Short Answer Type Questions I [2 Marks] Question 17. In figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region Solution:
  • 35. Expert’s class Ahmedabad Dhruv Thakar 8320495706 35 Question 18. In figure, OABC is a quadrant of a circle of radius 7 cm. If OD = 4 cm, find the area of the shaded region Solution: Short Answer Type Questions II [3 Marks] Question 19. In figure, a circle is inscribed in an equilateral triangle ABC of side 12 cm. Find the radius of inscribed circle and the area of the shaded region
  • 36. Expert’s class Ahmedabad Dhruv Thakar 8320495706 36 Solution: Question 20. In figure, PSR, RTQ and PAQ are three semicircles of diameters 10 cm, 3 cm and 7 cm respectively. Find the perimeter of the shaded region Solution:
  • 37. Expert’s class Ahmedabad Dhruv Thakar 8320495706 37 Question 21. In figure, two concentric circles with centre O, have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region Solution: Question 22. In figure, ABCD is a trapezium of area 24.5 sq. cm. In it, AD ¦ ¦ BC, ∠DAB = 90°, AD = 10 cm and BC = 4 cm. If ABE is a quadrant of a circle, find the area of the shaded region
  • 38. Expert’s class Ahmedabad Dhruv Thakar 8320495706 38 Solution: Question 23. In figure, ABDC is a quadrant of a circle of radius 28 cm and a semicircle BEC is drawn with BC as diameter. Find B the area of the shaded region. Solution:
  • 39. Expert’s class Ahmedabad Dhruv Thakar 8320495706 39 2013 Short Answer Type Questions I [2 Marks] Question 24. Two circular pieces of equal radii and maximum area,touching each other are cut out from a rectangular cardboard of dimensions 14 cm x 7 cm. Find the area of the remaining cardboard Solution: Question 25. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes. Solution: Question 26. In the given figure,the area of the shaded region between two concentric circles is 286 cm2.If the difference of the radii of the two circles is 7 cm, find the sum of their radii.
  • 40. Expert’s class Ahmedabad Dhruv Thakar 8320495706 40 Solution: Short Answer Type Questions II [3 Marks] Question 27. In the given figure AB and CD are two diameters of a circle with centre O,Which are perpendicular to each other.OB is the diameter of small circle.If OA=7cm,find area of shaded region Solution: Question 28. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find 1. the length of the arc 2. area of the sector formed by the arc.
  • 41. Expert’s class Ahmedabad Dhruv Thakar 8320495706 41 Solution: Question 29. In figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 21 cm, find the area of the shaded region Solution: Question 30. A chord of length 10 cm divides a circle of radius 5√2 cm in two segments. Find the area of the minor segment Solution:
  • 42. Expert’s class Ahmedabad Dhruv Thakar 8320495706 42 Question 31. In the given figure, from each corner of a square of side 4 cm, a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut. Find the area of the shaded region. Solution: 2012 Short Answer Type Questions I [2 Marks]
  • 43. Expert’s class Ahmedabad Dhruv Thakar 8320495706 43 Question 32. In figure, OABC is a square of side 7cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region Solution: Question 33. In figure, ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of the shaded region Solution: Refer to Ans 31. Question 34. From a rectangular sheet of paper ABCD with AB = 40 cm and AD = 28 cm, semicircular portion with BC as diameter is cut off. Find the area of the remaining paper. Solution:
  • 44. Expert’s class Ahmedabad Dhruv Thakar 8320495706 44 Question 35. In the given figure, the shape of the top of a table is that a sector of a circle with centre O and ∠AOB = 90°. If AO = OB = 42 cm,then find the perimeter of the top of the table Solution: Short Answer Type Questions II [3 Marks] Question 36. In figure, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and 3.5 cm and centre O. If ∠POQ = 30°, then find the area of the shaded region. Solution: Question 37. In figure, find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC are semicircles.
  • 45. Expert’s class Ahmedabad Dhruv Thakar 8320495706 45 Solution: Question 38. In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region. Solution: Question 39. Find the area of the shaded region in Figure, if ABCD is a square of side 28 cm and APD and BPC are semicircles.
  • 46. Expert’s class Ahmedabad Dhruv Thakar 8320495706 46 Solution: Question 40. In figure, ABCD is a square of side 7 cm. DPBA and DQBC are quadrants of circles, each of radius 7 cm. Find the area of the shaded region. Solution: side of square=7cm radius of circle=7cm
  • 47. Expert’s class Ahmedabad Dhruv Thakar 8320495706 47 Question 41. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 10 minutes Solution: 2011 Short Answer Type Questions I [2 Marks] Question 42. In figure APB and CQD are semicircles of diameter 7 cm each, while ARC and BSD are semicircles of diameter 14 cm each. Find the perimeter of the shaded region
  • 48. Expert’s class Ahmedabad Dhruv Thakar 8320495706 48 Solution: Question 43. Find the area of a quadrant of a circle, where the circumference of circle is 44cm Solution: Question 44. Find the perimeter of the shaded region in figure, if ABCD is a square of side 14 cm and APB and CPD are semicircles
  • 49. Expert’s class Ahmedabad Dhruv Thakar 8320495706 49 Solution: Question 45. In given figure, a semicircle is drawn with O as centre and AB as diameter. Semicircles are drawn with AO and OB as diameters.If AB = 28 m, find the perimeter of the shaded region Solution: Question 46. In given figure, ABC is a triangle right-angled atB, with AB = 14 cm and BC = 24 cm. With thevertices A, B and C as centres, arcs are drawn each of radius 7 cm. Find the area of the shaded region.
  • 50. Expert’s class Ahmedabad Dhruv Thakar 8320495706 50 Solution: Question 47. In the given figure, OABC is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region Solution: Short Answer Type Questions II [3 Marks] Question 48. Find the area of the major segment APB in figure of a circle of radius 35 cm and ∠AOB = 90°.
  • 51. Expert’s class Ahmedabad Dhruv Thakar 8320495706 51 Solution: Question 49. A chord of a circle of radius 14 cm subtends an angle of 120° at the centre. Find the area of the corresponding minor segment of the circle. Solution: Question 50. A chord of a circle of radius 21 cm subtends an angle of 60° at the centre. Find the area of the corresponding minor segment of the circle
  • 52. Expert’s class Ahmedabad Dhruv Thakar 8320495706 52 Solution: Question 51. Area of a sector of a circle of radius 14 cm is 154 cm². Find the length of the corresponding arc of the sector Solution: Question 52. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding minor segment and hence find the area of the major segment
  • 53. Expert’s class Ahmedabad Dhruv Thakar 8320495706 53 Solution: Long Answer Type Questions [4 Marks] Question 53. In figure, arcs are drawn by taking vertices A, B and C of an equilateral triangle ABC of side 14 cm as centres to intersect the sides BC, CA and AB at their respective mid-point D, E and E Find the area of the shaded region Solution: Question 54. The length and breadth of a rectangular piece of paper are 28 cm and 14 cm respectively. A semi-circular portion is cut off from the breadth’s side and a semicircular portion is added on length’s side, as shown in figure. Find the area of shaded region
  • 54. Expert’s class Ahmedabad Dhruv Thakar 8320495706 54 Solution: Question 55. Find the area of shaded region in figure,where arcs drawn with centres A,B,C and D intersects at mid point P,Q,R and S of sides AB,BC,CD and DA of a square ABCD,where the length of each side of square is 14 cm Solution: Question 56. In the given figure, three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area of shaded region
  • 55. Expert’s class Ahmedabad Dhruv Thakar 8320495706 55 enclosed between these three circles Solution: Question 57. In given figure, an equilateral triangle has been inscribed in a circle of radius 6 cm. Find the area of the shaded region. Solution:
  • 56. Expert’s class Ahmedabad Dhruv Thakar 8320495706 56 Question 58. Find the area of the shaded region in given figure, where ABCD is a square of side 28 cm Solution: Question 59. From a thin metallic piece, in the shape of a trapezium ABCD in which AB ¦¦ CD and ∠BCD = 90°, a quarter circle BFEC is removed (See figure). Given AB = BC = 3.5 cm and DE = 2 cm, calculate the area of the remaining (shaded) part of the metal sheet.
  • 57. Expert’s class Ahmedabad Dhruv Thakar 8320495706 57 Solution: 2010 Short Answer Type Questions II [3 Marks] Question 60. In figure, the boundary of shaded region consists of four semicircular arcs, two smallest being equal. If diameter of the largest is 14 cm and that of the smallest is 3.5 cm, calculate the area of the shaded region.
  • 58. Expert’s class Ahmedabad Dhruv Thakar 8320495706 58 Solution: Question 61. Find the area of the shaded region in figure, if AC = 24 cm, BC = 10 cm and O is the centre of the circle Solution: Question 62. In figure, AB and CD are two perpendicular diameters of a circle with centre
  • 59. Expert’s class Ahmedabad Dhruv Thakar 8320495706 59 O. If OA = 7 cm, find the area of the shaded region Solution: Question 63. Find the area of the shaded region in figure, where a circular arc of radius 7 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm, as centre Solution:
  • 60. Expert’s class Ahmedabad Dhruv Thakar 8320495706 60