chapter 12.4 and 12.5 volume of prisms, cylinders, pyramids, and cones

Chapter 12.4 and 12.5Volume of Prisms, Cylinders, Pyramids, and Cones

Volume Volume of a solid is the measure of

the amount of space the solid encloses.

Volume is measured in cubic units.

Concept

Example 1Volume of a Prism

Answer: The volume of the prism is 1500 cubic centimeters.

Find the volume of the prism.

Example 1

A. 6480 in3

B. 8100 in3

C. 3240 in3

D. 4050 in3

Find the volume of the prism.

Concept

Example 2Volume of a Cylinder

Find the volume of the cylinder to the nearest tenth.

Answer: The volume is approximately 18.3 cm3.

Example 2

A. 62.8 cm3

B. 628.3 cm3

C. 125.7 cm3

D. 1005.3 cm3

Find the volume of the cylinder to the nearest tenth.

Example 3Volume of an Oblique Solid

Find the volume of the oblique cylinder to the nearest tenth.

Answer: The volume is approximately 17,671.5 cubic feet.

Example 3

A. 1520.5 cm3

B. 16,725.8 cm3

C. 5324 cm3

D. 8362.9 cm3

Find the volume of the oblique cylinder to the nearest tenth.

Example 4Prisms A and B have the same width and height, but different lengths. If the volume of Prism B is 128 cubic inches greater than the volume of Prism A,what is the length of each prism?

A 12 B 8

C 4 D 3.5

Prism A Prism B

Comparing Volumes of Solids

Example 4

A. 4 in.

B. 6 in.

C. 8 in.

D. 10.5 in.

Prisms A and B have the same width and height, but different lengths. If the volume of Prism B is 192 cubic inches greater than the volume of Prism A,what is the length of each prism?

Prism A

Prism B

Concept

Example 1Volume of a Pyramid

Find the volume of the square pyramid.

Answer: The volume of the pyramid is 21 cubic inches.

Example 1Brad is building a model pyramid for a social studies project. The model is a square pyramid with a base edge of 8 feet and a height of 6.5 feet. Find the volume of the pyramid.

A. 416 ft3

B.

C.

D.

Concept

Example 2AVolume of a Cone

A. Find the volume of the oblique cone to the nearest tenth.

Example 2BVolume of a Cone

B. Find the volume of the cone to the nearest tenth.

Example 2A

A. 444.4 m3

B. 27,463.2 m3

C. 3051.5 m3

D. 9154.4 m3

A. Find the volume of the oblique cone to the nearest tenth.

Example 2B

A. 3015.9 m3

B. 125.7 m3

C. 1005.3 m3

D. 251.3 m3

B. Find the volume of the cone to the nearest tenth.

Example 3Find Real-World Volumes

SCULPTURE At the top of a stone tower is a pyramidion in the shape of a square pyramid. This pyramid has a height of 52.5 centimeters and the base edges are 36 centimeters. What is the volume of the pyramidion? Round to the nearest tenth.

Answer: The volume of the pyramidion is 22,680 cubic centimeters.

Example 3

A. 18,775 cm3

B. 19,500 cm3

C. 20,050 cm3

D. 21,000 cm3

SCULPTURE In a botanical garden is a silver pyramidion in the shape of a square pyramid. This pyramid has a height of 65 centimeters and the base edges are 30 centimeters. What is the volume of the pyramidion? Round to the nearest tenth.

Concept