1. Geometry 10-5 Volume of Prisms and Cylinders

2. Warm-Up Exercises 1 question Many, Many Answers

3. Volume So far we have studied length and area, now we are moving into the last topic in geometry, volume Make a list of occupations that work with quantities that are measured by volume. The longest list wins

4. Answers

5. Volume Pharmacists Plumber Carpenter Biologist Painters Grocers Chemists Engineers Gas Station Blood Mobile

6. Vocabulary Volume – The amount of space contained inside a solid. Measured as a cubic. Like m 3 or ft 3

7. New Material

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

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

10. Volume of a Prism

11. Volume Exploration As a group, agree upon the volume of a stack of computer paper

12. Volume Exploration What fills up this volume If you knew how many pages were in the stack, could calculate the volume of one piece?

13. Volume Exploration What happens when we slant the stack? Has the volume changed? Has the height changed?

14. 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

15. Cavalieri’s Principle

16. Volume of a Cylinder Based on your knowledge of the volume of a prism, what is the volume of a cylinder?

17. Volume of a Cylinder The volume V of a cylinder is V = Bh = πr 2 h where B is the area of a base, h is the height, and r is the radius of a base Regardless of whether or not it is a right cylinder

18. Volume of a Cylinder The volume V of a cylinder is V = Bh = πr 2 h where B is the area of a base, h is the height, and r is the radius of a base

19. Example

26. Sample Problems

27. 2061.2 cm 3

28. 540 in 3

29. 477.5 cm 3

30. 72

31. 378

32. 64

33. 144 in 3

34. 62.35 m 3

35. 12 ft 3

36. 520 ft 3

37. 140.3 in 3

38. Practice Problems

46. Homework Pages 547 – 550 2 – 12 even, 17, 26, 33, 34, 46

47. Honors Homework Pages 547 – 550 2 – 12 even, 17, 26, 30, 31, 33, 34, 46