# Volumes of Prisms and Cylinders Find volumes of

• Slides: 15

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 h Area of base = B

Example 1 Volume of a Triangular Prism Find the volume of the triangular prism. 17 cm 8 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. ) = 250 ft. 3 (250 ft. 3)(6. 9 lb. /ft. 3)= 1725 lb. 25 ft. 1 ft. 10 ft.

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 r Area of base = r 2

Example 3 Volume of a Cylinder Find the volume of the cylinder. 12. 4 m 4. 6 m

Example 4 Volume 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 crosssectional area at the same level, then they have the same volume.

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