Volume of Prisms and Cylinders

Volume of Prisms and Cylinders

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Definition

Volume - the amount of space that an object occupies/contains

How to find the Volume of a Prism

Volume is equal to the "area of the Base" times "height"

V = Bh

B -> Area of the base shape

-> different from lowercase b (base of the shape)

Multiple Choice

The volume formulas of a cylinder and prism are the SAME.

• True

• False

Multiple Choice

The volume formula of a prism is...

• V = 2Bh

• V = ½Bh

• V = Bh

• V = Bh²

Example 1

The area of the hexagonal base of this prism is 23 in². The height of the prism is 7 in. What is the volume of the prism?

V = Bh

V = (23) * (7)

V = 161 in³

Multiple Choice

In the diagram, the area of the pentagonal base is 43 mm². Find the volume of the pentagonal prism.

• 129 mm³

• 345 mm³

• 645 mm³

• 27,735mm³

Multiple Choice

The volume formula of a cylinder is...

• V = πr²

• V = Bhπ

• V = Bh

• V = πh²

Example 2

Example 3

Multiple Choice

What is the volume of this cylinder?

• 42π in³

• 21π in³

• 63π in³

• 84π in³

Multiple Choice

The volume of a cylinder is 396 $$\pi$$ cubic inches.  The height of the cylinder is 11 inches.  What is the diameter of the cylinder?

• 6 inches

• 12 inches

• 3 inches

• 17 inches

Multiple Choice

This trough is filled with water.  If 1 cubic foot holds  7.5 gallons, how much water will fill the trough?

• 21.5 gallons
• 112.5 gallons
• 133 gallons
• 150 gallons

Multiple Choice

Find the height of a tissue box if the volume of a tissue box is 3140.28 cm³ and length is 22 cm and width is 12.2 cm.

• 11.7 cm

• 12 cm

• 34.2 cm

• 45.9 cm