cone and sphere
Download as PPTX, PDF1 like433 views
The document provides information about geometric shapes including cones, spheres, and examples of calculating their properties. It defines formulas for calculating the surface area and volume of cones and spheres. It gives two examples, one calculating the curved surface area, base area, and total surface area of a cone with a 10cm base diameter and 12cm height. The other calculates the volume and surface area of a sphere with radius 14cm. An exercise at the end asks the reader to use the formulas to find properties of additional shapes.
cone and sphere
- 1. PHALOSA Norma Trialisa Rina Fauziah Selviane Andini Silvia Refina Dewi Widyaestifa Adinugraheni Yeshie Agustin Fadhilah
- 2. CONE
- 4. The net of cone s s 2 r ..…… r
- 5. The surface Area of Cone How To find the surface Area of The cone? To find the surface area of the cone, we need to calculate all the areas of the laterals. So, we need to find: the area of curved area and circle area
- 6. Surface Area of Cone Area of sector = Circumference of base Area of big circle = Circumference of big . circle L = area of sector Area of sector = A B r = ----- --- = Base = The surface area of cone (SA) equals the sum of the area of the sector ( or lateral face) (LA )and the area of the base (B) Surface Area of Cone SA = LA + B = π r s + π r² = π r (s + r)
- 7. π r2 h 1/3 π r2h 1/3 π r2h 1/3 π r2h
- 8. The Volume of Cone V= B. h V=
- 9. SPHERE
- 10. Center of sphere Point O is the center of the sphere. A ----------- C Point AO is the radii of the sphere. AC is one of the diameter in the B sphere. Sphere only has one curved surface. Sphere doesn’t have a vertex nor an edge. The Radius of sphere
- 11. Surface Area of Sphere • Formula of the surface of a sphere : A = 4 π r²
- 12. Volume of Sphere Formula of the volume of a sphere : V = π r³
- 13. THE EXAMPLES
- 14. The Cone • A cone has a base plane diameter of 10 cm and height of 12 cm. For π = 3.14 : a. The curved surface area b. The base area c. The surface area SOLUTION
- 15. Given that : d = 10 cm h = 12 cm π = 3.14 • s = √h² + r² = √12² + 5² = √144 + 25 = √ 169 ↔ s = 13 cm a. The curved surface area = π r s = 3.14 x 5 x 13 = 204.1 cm² b. The base area = π r² = 3.14 x 5 x 5 = 78.5 cm²
- 16. c. The surface area = A of cs + ba = 204.1 + 78.5 = 282.6 cm²
- 17. The Sphere Given that : r =14 cm π = 22/7 Asked : Volume? Surface Area? SOLUTION
- 18. Volume = 4/3 x π x r³ = 4/3 x 22/7 x 14³ = 4/3 x 22/7 x 2744 = 4/3 x 22 x 392 = 11498.7 cm³ Surface Area = 4 . π . r² = 4 . 22/7 . 14² = 4 . 22 . 28 = 88 . 28 = 2464 cm²
- 19. EXERCISE 1. A cone has a base radius of 7cm. If the area of its curved surface is 550cm² and π = 22 , find: 7 a. The slant height b. The surface area c. The height of cone
- 20. Solution a. Cs =πrl 22 550 = 7 x7xl 550 = 22s 550 s = 22 l = 25cm b. SA = π r (l+r) 22 = 7 x 7 x (25+7) = 22 x 32 704 cm² c. h = √l² - r² = √25² - 7² = √576 h = 24cm
- 21. 2. Find the radius of the sphere of which the surface area is 2826 cm² and π 3.14
- 22. Solution Given that : Sa = 2826 cm² π = 3.14 Asked : r = ? Answer : Sa = 4 π r² 2826 = 4 x 3.14 x r² 900 r = √2826 4 x 3.14 r = √225 r = 15 cm
- 23. “You only life once but if you do it right, once is enough “ - Maewest -
- 24. THANK YOU