1. 1 cm
1 cm
1 cm

2. Volume
The volume of a three-dimensional figure is the number of cubic units needed to fill the figure.

3. 2 cm
3 cm
2 cm

4. Formula: Volume of a Prism
V = BH The volume of a prism (V) is equal to the area of the base (B) times the height (H).

5. Example 1
Find the volume of a rectangular prism that has a 5 ft. × 9 ft. rectangular base and whose height is 2.5 ft.
V = BH
B = 5(9)
= 45
V = BH
= 45(2.5)
= ft.3

6. Example 2 Find the volume of the triangular prism. V = BH B = (12)(9)
15 cm
V = BH
10 cm
B = (12)(9)
1 2
9 cm
= 54
12 cm
V = BH
= 54(10)
= 540 cm3

7. Example Find the height of the prism below if its volume is 168 m3.

8. Example
Find the volume of a rectangular prism with l = 10 units, w = 5 units, and h = 3 units.
150 units3

9. The new volume is 8 times the original.
Example
What happens to the volume of a cube if the length of its sides is doubled?
The new volume is 8 times the original.

10. Formula: Volume of a Circular Cylinder
V = BH The volume of a = pr2H circular cylinder (V) is equal to the area of the base (B) times the height (H). Substitute for B.

11. Example 3 Find the volume of the cylinder. V = BH = pr2H = p(42)(7)
4 cm
= pr2H
= p(42)(7)
7 cm
= 112p
= 112(3.14)
≈ cm3

12. Example 4
Find the radius of a cylinder with a height of 12 ft. and a volume of 432p ft.3.
V = pr2H
432p = pr2(12)
36 = r2
±6 = r
r = 6 ft.

13. Example
Find the volume of a circular cylinder with a radius of 4.5 cm and a height of 6 cm.
cm3

14. Example
What is the radius of a circular cylinder if its volume is 3,077.2 units3 and its height is 20 units?
7 units

15. The new volume is 8 times the original.
Example
What happens to the volume of a circular cylinder if both its dimensions (height and radius) are doubled?
The new volume is 8 times the original.