Volumes of Prisms and Cylinders

1. Volumes of Prisms and Cylinders • Find volumes of prisms. • Find volumes of cylinders.

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6. 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.

7. Key ConceptVolume 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

8. Example 1Volume of a Triangular Prism Find the volume of the triangular prism. 17 cm 8 cm 13 cm a

9. Example 2Volume 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.

10. 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.

11. Key ConceptVolume 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 r Area of base = r2

12. Example 3Volume of a Cylinder Find the volume of the cylinder. 12.4 m 4.6 m

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

14. Key ConceptCavalieri’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.

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