1. Volumes of Pyramids and Cones
Geometry 10-6

2. Review

3. The volume of a cube is the cube of the length of its side, or V=s3

4. Volume Addition Postulate
The volume of a solid is the sum of the volumes of all its non-overlapping parts
Volume Addition Postulate

5. The volume V of a prism is V = Bh, where B is the area of a base and h is the height
Volume of a Prism

6. Volume of a Cylinder The volume V of a cylinder is V = Bh = πr2h
where B is the area of a base, h is the height, and r is the radius of a base
Volume of a Cylinder

7. Cavalieri’s Principle
If two solids have the same height and the same cross-sectional area at every level, then they have the same volume
Cavalieri’s Principle

8. New Material

9. Pyramid Exploration Get your supplies Paper Scissors
Marker or color pencil
Pyramid Exploration

10. Pyramid Exploration Draw a net for a six sided prism on your paper
Cut it out
Fold and tape it into a prism
Pyramid Exploration

11. Using one side for a base, take your prism, and outline and color a section that would be a right pyramid with the same height as the prism
Color the sides that would be part of the pyramid, as shown
Pyramid Exploration

12. Using an uncolored side as a base, make another right pyramid with the same height as the prism
Color the sides that would be part of the pyramid, a different color
Pyramid Exploration

13. Pyramid Exploration What is left, that has not been colored in?
Do you think this would work even if the pyramids were not right pyramids?
Pyramid Exploration

14. Would this work even if the base of the pyramid was not a rectangle?
Pyramid Exploration

15. Volume of a Pyramid The volume V of a pyramid is V = 1/3 Bh
where B is the area of a base, h is the height
Volume of a Pyramid

16. Volume of a Pyramid The volume V of a pyramid is V = 1/3 Bh
where B is the area of a base, h is the height
Volume of a Pyramid

17. Cone Volume When we solved for the volume of a pyramid
Did it matter how many sides the pyramid had?
Cone Volume

18. What if we kept increasing the number of sides of the pyramid, and the corresponding prism
what shapes do they become?
Cone Volume

19. Volume of a Cone The volume V of a cone is V = 1/3 Bh V = 1/3 πr2h
where B is the area of a base, h is the height and r is the radius of the cone
Volume of a Cone

20. Volume of a Cone The volume V of a cone is V = 1/3 Bh V = 1/3 πr2h
where B is the area of a base, h is the height and r is the radius of the cone
Volume of a Cone

21. Example

22. Example

23. Example

24. Example

25. Example

26. Sample Problems

31. 64 units3

32. 70 2/3 cm3

33. in3

34. 64 units3

35. 70 2/3 cm3

36. in3

37. Practice Problems

38. Practice Problems

39. Practice Problems

40. Practice Problems

41. Practice Problems

42. Practice Problems

43. Practice Problems

44. Practice Problems

45. Pages 554 – 557
6 – 18 even, 19, 22, 23, 43
Homework