Learn and apply the formula for the volume of a sphere.
- 1. Holt Geometry 10-8 Spheres Warm Up Find each measurement. 1. the radius of circle M if the diameter is 25 cm 2. the circumference of circle X if the radius is 42.5 in. 3. the area of circle T if the diameter is 26 ft 4. the circumference of circle N if the area is 625 cm2 12.5 cm 85 in. 169 ft2 50 cm
- 2. Holt Geometry 10-8 Spheres • Learn and apply the formula for the volume of a sphere. • Learn and apply the formula for the surface area of a sphere. Objectives
- 3. Holt Geometry 10-8 Spheres • A sphere is the locus of points in space that are a fixed distance from a given point called the center of a sphere. • A radius of a sphere connects the center of the sphere to any point on the sphere. • A hemisphere is half of a sphere. • A great circle divides a sphere into two hemispheres
- 5. Holt Geometry 10-8 Spheres Example 1A: Finding Volumes of Spheres Find the volume of the sphere. Give your answer in terms of . = 2304 in3 Simplify. Volume of a sphere.
- 6. Holt Geometry 10-8 Spheres Example 1B: Finding Volumes of Spheres Find the diameter of a sphere with volume 36,000 cm3 . Substitute 36,000 for V. 27,000 = r3 r = 30 d = 60 cm d = 2r Take the cube root of both sides. Volume of a sphere.
- 7. Holt Geometry 10-8 Spheres Example 1C: Finding Volumes of Spheres Find the volume of the hemisphere. Volume of a hemisphere Substitute 15 for r. = 2250 m3 Simplify.
- 8. Holt Geometry 10-8 Spheres Example 3A: Finding Surface Area of Spheres Find the surface area of a sphere with diameter 76 cm. Give your answers in terms of . S = 4r2 S = 4(38)2 = 5776 cm2 Surface area of a sphere
- 9. Holt Geometry 10-8 Spheres Example 3B: Finding Surface Area of Spheres Find the volume of a sphere with surface area 324 in2 . Give your answers in terms of . Substitute 324 for S. 324 = 4r2 r = 9 Solve for r. Substitute 9 for r. The volume of the sphere is 972 in2 . S = 4r2 Surface area of a sphere
- 10. Holt Geometry 10-8 Spheres Example 3C: Finding Surface Area of Spheres Find the surface area of a sphere with a great circle that has an area of 49 mi2 . Substitute 49 for A. 49 = r2 r = 7 Solve for r. S = 4r2 = 4(7)2 = 196 mi2 Substitute 7 for r. A = r2 Area of a circle
- 11. Holt Geometry 10-8 Spheres Lesson Quiz: Part I Find each measurement. Give your answers in terms of . 1. the volume and surface area of the sphere 2. the volume and surface area of a sphere with great circle area 36 in2 3. the volume and surface area of the hemisphere V = 36 cm3 ; S = 36 cm2 V = 288 in3 ; S = 144 in2 V = 23,958 ft3 ; S = 3267 ft2
- 12. Holt Geometry 10-8 Spheres Lesson Quiz: Part II 4. A sphere has radius 4. If the radius is multiplied by 5, describe what happens to the surface area. 5. Find the volume and surface area of the composite figure. Give your answer in terms of . The surface area is multiplied by 25. V = 522 ft3 ; S = 267 ft2