6th Grade Math Textbook, Fundamentals

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11-7

Think

The length, width, and height of a

1-inch cube each measure 1 inch.

So the volume of a 1-inch cube is

1 cubic inch, or 1 in.^3

1 • 1 • 1 is “1 to the third power” or

“1 cubed.”

Volume of Prisms

Objective To use a formula to find the volume of a rectangular prism• To use a formula to find

the volume of a triangular prism• To find an unknown dimension given the volume of a rectangular

prism or a triangular prism• To rename volume units in equivalent forms

A fish tank in the shape of a rectangular prism is 30 inches
long, 15 inches wide, and 16 inches high. How much water is
needed to fill the tank completely?

To find how much water is needed to fill the tank, find the
volumeof the tank.

The of a three-dimensional figure is the amount

of space it occupies or contains. Volume is measured in

—for example, cubic centimeters (cm^3 ) or

cubic feet (ft^3 ).

Method 1 Use Unit Cubes

One way to find the volume is to count the number of

unit cubes the tank could hold. Imagine making a layer

of 1-inch cubes on the bottom of the tank. The layer would

be 30 cubes long and 15 cubes wide. So the layer would

contain 30 • 15 cubes, or 450 cubes. Since the height of

the tank is 16 inches, you would need 16 layers to fill the

tank for a total of 16 • 450 cubes, or 7200 cubes.

Method 2 Use a Formula

To find the number of cubes needed to fill the tank,

you multiplied the length (30 cubes), width (15 cubes),

and height (16 cubes).

Use the formula: Vwh

30 • 15 • 16

 7200

So the volume of the tank is 7200 cubic inches, or 7200 in.^3

Another way to think about finding the

volume of the rectangular prism is to think

about multiplying the area of the base (w)

by the height (h). This process leads to the

formula for the volume of a triangular prism.

cubic units

volume

30 cubes long

15 cubes wide

Stack 16 layers to fill the tank.

 30 in.

w 15 in.

h 16 in.

Key Concept

Vwh, where Vvolume, length,

wwidth, and hheight

The formula can also be expressed as

VBh, where Brepresents the area of

the base and hrepresents the height.

Volume (V) of a Rectangular Prism

Key Concept

VBh, where Vvolume,

Barea of the base, and

hheight

Volume (V) of a Triangular Prism