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The volume of a prism is the number of cubic units required to fill the solid figure. Volume is measured in cubic units. They are called cubic units because they are little cubes that are one unit long, one unit wide, and one unit high. They could be any unit of measure; inches, centimeters, feet, yards, etc.

Unit of Length	Unit of Volume
Inches	Cubic Inches
Centimeters	Cubic centimeters
Feet	Cubic feet

To find the volume of a rectangular prism, count the number of cubic units in one layer, count the number of layers needed to completely fill the figure, and then multiply them together.

Example: Find the volume of the rectangular prism.

Left figure has the bottom of a rectangular prism with one layer of cubes, right figure has the prism completely filled with cubes.

Answer the following questions using the figures in the illustration above. Click on the blank space to check your answers.

How many cubic units are needed for one layer?
Interactive popup. Assistance may be required.
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24
How many layers are needed to fill the rectangular prism?
Interactive popup. Assistance may be required.
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8
Multiply the cubic units in one layer by the number of layers needed to fill the prism.
Interactive popup. Assistance may be required.
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24 x 8 = 192
One way to find the number of cubic units in one layer is to multiply the length by width. This is called the Interactive popup. Assistance may be required. _______________ area of the rectangle.

The number of layers to fill the prism is called the Interactive popup. Assistance may be required. _______________ height of the prism.
Using the above information, the formula for the volume of a prism is
Interactive popup. Assistance may be required.
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V = l x w x h = Bh

An upper case B is used to represent the area of the base of the prism.

The formula for the volume of the prism is:

Each variable in the surface area formula is identified

**Lower case b and h are the length and height of an individual polygon. Upper case B refers to the area of a polygonal base of the prism.

Prisms are named according to the shape of their base. A prism's base can be any polygon. The upper case B refers to the area of any shape of the base.