Volume of Pyramids and Cones

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Presentation transcript:

Volume of Pyramids and Cones GEOMETRY LESSON 10-6 10. about 562.9 ft3 11. ft3; 17 ft3 12. in.3; 23 in.3 13. 36.75 in.3; 115 in.3 14. about 66.4 cm3 15. about 4.7 cm3 16. 123 in.3 17. 312 cm3 18. 10,368 ft3 19. They are equal; both volumes are r2h 20. a. 6,312,000 ft3 b. 284 ft 21. 6 22. 3 23. 3 2 1. about 233,333 ft3 2. 200 cm3 3. 1296 in.3 4. 50 m3 5. about 443.7 cm3 6. 300 in.3 7. 2048 m3 8. about 363.6 m3 9. about 3714.5 mm3 16 3 22 1 Pages 554-557 Exercises 10-6

Volume of Pyramids and Cones GEOMETRY LESSON 10-6 24. 73 cm3 25. Answers may vary. Sample: h = 50 in., r = 6 in.; h = 18 in., r = 10 in. 26. cube: 8 units3, cone: units3, pyramid: units3 27. a. 120 ft3 b. 60 ft3 c. 240 ft3 2 3 8 28. cone: 234.6 in.3; prism: 240 in.3; pyramid: 256 in.3 29. cone with r = 4 and h = 3; 16 30. cone with r = 3 and h = 4; 12 31. cylinder with r = 4, h = 3, with a cone of r = 4, h = 3 removed from it; 32 32. cylinder with r = 4, h = 5 with a cone of r = 1, h = 1 cut off the top, and a cylinder of r = 1 cut out of its center; 24 33. a. The frustum has vol. V = R2h – r2h = (R2h – r2h). Now if h1 = H – h is the 1 10-6

Volume of Pyramids and Cones GEOMETRY LESSON 10-6 33. a. (continued) frustum’s height, V = (R2(h1 + h) – R2h) = (R2 h1 + h(R2 – r2)). By similar , = , or h = Simplifying, V = h1(r2 + rR + R2). b. about 784.6 in.3 34. a. 47.1 m b. 176.7 m2 c. 389.6 m3 35. about 16.2 cm 36. about 8.8 cm 37. A 38. F 39. A 40. F 41. A 42. [2] d = r; r = (203) = 101.5; V = r2h, so 1 3 1 3 h1 + h R rh1 R – r h r . s 1 3 1 2 1 2 1 3 10-6

Volume of Pyramids and Cones GEOMETRY LESSON 10-6 42. [2] (continued) 82,418 = (101.5)2h and h = 24 cm. [1] one computational error 43. 7.1 in.3 44. 3600 cm3 45. 59.4 in.2 46. 62.4 cm2 1 3 47. 57.7 in.2 48. 13.9 cm2 10-6