Volume is calculated by multiplying the area of the base by the height of the object. The area of a two-dimensional shape is calculated by multiplying its length and width. The volume of a three-dimensional object considers its length, width, and height. Several examples are provided to demonstrate calculating the volume of prisms and cylinders by finding the area of their base and multiplying it by the height.

1. VOLUME

2. Area is a measure of 2 dimensions: Length & Width

3. You can find the area of any FLAT shape. 5 cm 11 cm 5 x 11 = 55 cm 2

4. Volume is a measure of 3 dimensions: LENGTH, WIDTH, & HEIGHT

5. Imagine starting with a piece of rectangular paper. 3 cm 4 cm

6. The area of this rectangle is 12 square cmches 3 cm 4 cm

7. Now, suppose that we “stacked” another piece of paper on top of this piece of paper. 3 cm 4 cm

8. 3 cm 4 cm

9. 3 cm 4 cm

10. 3 cm 4 cm

11. 3 cm 4 cm

12. 3 cm 4 cm Now we have 2 pieces of paper, each with an area of 12. So the volume is 24.

13. 3 cm 4 cm Let’s add another piece of paper to the stack.

14. 3 cm 4 cm

15. 3 cm 4 cm

16. 3 cm 4 cm

17. 3 cm 4 cm

18. 3 cm 4 cm

19. 3 cm 4 cm Now we have 3 pieces of paper, each with an area of 12. So the volume is 36.

20. If we had 10 pieces of paper stacked on top of one another, what would the volume be? 4 cm 3 cm 10

21. 4 x 3 x 10 = 120 cm 3 4 cm 3 cm 10

22. Practice Time!

23. Calculate the volume of this prism. 5 cm 8 cm 6 cm

24. The volume is 240 cubic cm. 6 x 5 x 8 5 cm 8 cm 6 cm

25. Calculate the volume of this prism. 3 cm 12 cm 5 cm

26. The volume is 180 cubic cm. 5 x 3 x 12 3 cm 12 cm 5 cm

27. Calculate the volume of this prism. 4 cm 11 cm 7 cm

28. The volume is 308 cubic cm. 7 x 4 x 11 4 cm 11 cm 7 cm

29. Volume can also be described as AREA x Height

30. Suppose that the area of this rectangle is 12. 4 3

31. Suppose that this rectangle served as the base of a rectangular prism.

32. Suppose that the prism has a height of 2. 2

33. 2

34. 2

35. If the area (length x width) of the base is 12, and the height is 2… 2

36. then the volume should be 24 cubic units. 2

37. SUMMARY Volume = Length x Width x Height or Volume = Area of Base x Height

38. Practice Time!

39. 1) Find the volume of the prism. 3 cm 3 cm 8 cm

40. The volume is 72 cm 3 . 3 x 8 x 3 3 cm 3 cm 8 cm

41. 2) Find the volume of the prism. 5 cm 5 cm 12 cm

42. The volume is 300 cm 3 . 12 x 5 x 5 5 cm 5 cm 12 cm

43. 3) Find the volume of the prism. 2.5 m Area = 20 m 2 base base

44. Volume = area x height Volume = 20 x 2.5 = 50 m 3 2.5 m Area = 20 m 2 base base

45. 4) Find the volume of the prism. 14 m Area = 12 m 2 base base

46. Volume = area x height Volume = 12 x 14 = 168 m 3 14 m Area = 12 m 2 base base

47. 5) Find the volume of the prism. 25 cm Area = 15 cm 2 base base

48. Volume = area x height Volume = 15 x 25 = 375 cm 3 25 cm Area = 15 cm 2 base base

49. 6) Find the volume of the cylinder. 10 cm Area = 78.5 cm 2 base base

50. Volume = area x height Volume = 78.5 x 10 = 785 cm 3 10 cm Area = 78.5 cm 2 base base

51. 7) Find the volume of shape. 12 m Area = 36.2 m 2 base base

52. Volume = area x height Volume = 36.2 x 12 = 434.4 m 3 12 m Area = 36.2 m 2 base base