Volumes of Prisms and Cylinders– Find volumes of prisms.– Find volumes of cylinders.

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VOLUMES OF PRISMSThe volume of a figure is the measure of the amount of space that the figure encloses. Volume is measured in cubic units.

Key Concept Volume of a Prism

If a prism has a volume of V cubic units, a height of h units, and each base has a area of B square units, then

V = Bh

Area of base = B

h

Example 1 Volume of a Triangular PrismFind the volume of the triangular prism.

8 cm

17 cm

13 cm

a

Example 2 Volume of a Rectangular PrismSNOW The weight of wet snow is 6.9 pounds per cubic foot. How many pounds of wet snow would a person shovel from a rectangular driveway 25 feet by 10 feet after 1 foot of snow has fallen?

1 ft.10 ft.

25 ft.

(1 ft.)(10 ft.)(25 ft.) = 250 ft.3

(250 ft.3)(6.9 lb./ft.3)= 1725 lb.

VOLUMES OF CYLINDERSLike the volume of a prism, the volume of a cylinder the product of the area of the base and the height.

Key Concept Volume of a Cylinder

If a cylinder has a volume of V cubic units, a height of h units, and the bases have radii R square units, then

V = Bh or V = r2h

Area of base = r2

r

Example 3 Volume of a CylinderFind the volume of the cylinder.

12.4 m

4.6 m

Example 4 Volume of a CylinderFind the volume of the cylinder.

5 in.

13 in.

Key Concept Cavalieri’s PrincipleIf two solids have the same height and the same cross-sectional area at the same level, then they have the same volume.

Example 5 Volume of an Oblique Cylinder

9 yd.

4 yd.