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

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VOLUMES OF PRISMS The 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 Prism Find the volume of the triangular prism. 8 cm 17 cm 13 cm a

Example 2 Volume of a Rectangular Prism SNOW 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 CYLINDERS Like 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 =  r 2 h Area of base =  r 2 r

Example 3Volume of a Cylinder Find the volume of the cylinder m 4.6 m

Example 4Volume of a Cylinder Find the volume of the cylinder. 5 in. 13 in.

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

Example 5Volume of an Oblique Cylinder 9 yd. 4 yd.