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Geometry Section 12-5
- 1. Section 12-5 Volumes ofPyramids and Cones
- 2. Essential Questions • Howdo you find volumes of pyramids? • How do you find volumes of cones?
- 3. Volume of aPyramid
- 4. Volume of aPyramid V = 1 3 Bh
- 5. Volume of aPyramid B = area of the base V = 1 3 Bh
- 6. Volume of aPyramid B = area of the base h = height of the pyramid V = 1 3 Bh
- 7. Example 1 Find thevolume of the pyramid.
- 8. Example 1 Find thevolume of the pyramid. V = 1 3 Bh
- 9. Example 1 Find thevolume of the pyramid. V = 1 3 Bh B = area of the square base
- 10. Example 1 Find thevolume of the pyramid. V = 1 3 Bh B = area of the square base V = 1 3 (3)2 (7)
- 11. Example 1 Find thevolume of the pyramid. V = 1 3 Bh B = area of the square base V = 1 3 (3)2 (7) V = 21 in3
- 12. Volume of aCone
- 13. Volume of aCone V = 1 3 Bh or V = 1 3 πr2 h
- 14. Volume of aCone V = 1 3 Bh or V = 1 3 πr2 h B = area of the base: B = πr2
- 15. Volume of aCone h = height of the cone V = 1 3 Bh or V = 1 3 πr2 h B = area of the base: B = πr2
- 16. Example 2 Find thevolume of the cone to the nearest hundredth.
- 17. Example 2 Find thevolume of the cone to the nearest hundredth. V = 1 3 πr2 h
- 18. Example 2 Find thevolume of the cone to the nearest hundredth. V = 1 3 πr2 h V = 1 3 π(5)2 (12)
- 19. Example 2 Find thevolume of the cone to the nearest hundredth. V = 1 3 πr2 h V = 1 3 π(5)2 (12) V ≈ 314.16 cm3
- 20. Example 3 Find thevolume of the cone to the nearest hundredth.
- 21. Example 3 Find thevolume of the cone to the nearest hundredth. V = 1 3 πr2 h
- 22. Example 3 Find thevolume of the cone to the nearest hundredth. V = 1 3 πr2 h V = 1 3 π(3.5)2 (13)
- 23. Example 3 Find thevolume of the cone to the nearest hundredth. V = 1 3 πr2 h V = 1 3 π(3.5)2 (13) V ≈166.77 ft3
- 24. Example 4 At thetop of a stone tower is a pyramidion in the shape of a square pyramid. The pyramid has a height of 52.5 centimeters and the base edges are 36 centimeters. What is the volume of the pyramidion rounded to the nearest hundredth?
- 25. Example 4 At thetop of a stone tower is a pyramidion in the shape of a square pyramid. The pyramid has a height of 52.5 centimeters and the base edges are 36 centimeters. What is the volume of the pyramidion rounded to the nearest hundredth? V = 1 3 Bh
- 26. Example 4 At thetop of a stone tower is a pyramidion in the shape of a square pyramid. The pyramid has a height of 52.5 centimeters and the base edges are 36 centimeters. What is the volume of the pyramidion rounded to the nearest hundredth? V = 1 3 Bh V = 1 3 (36)2 (52.5)
- 27. Example 4 At thetop of a stone tower is a pyramidion in the shape of a square pyramid. The pyramid has a height of 52.5 centimeters and the base edges are 36 centimeters. What is the volume of the pyramidion rounded to the nearest hundredth? V = 1 3 Bh V = 1 3 (36)2 (52.5) V = 22680 cm3
- 28.
- 29. Problem Set p. 860#1-12, 17, 18 all; skip #2, 6 “From a small seed a mighty trunk may grow.” - Aeschylus