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Volume of Rectangular Prisms

Volume of Rectangular Prisms

Cube - ColorIntroduction: Image you have a cardboard box and you want to know how much it can hold. With a ruler or meterstick you could calculate the volume of the box. If you measure one side of the base of the box you would have its length. Measure the width of the base and multiply it by the length and you will have the area of the box's base. So how do you find its volume?

A rectangular prism is a solid shape with six rectangular faces. A rectangular prism can be measured in three directions: length, width, and height. So, measure the length, width, and height of your cardboard box. Then, multiply all three numbers to find its volume. The formula for the volume of a rectangular prism is:

  • [math]"Volume"="Length"xx"Width"xx"Height"[/math]

This formula is often shorted to: [math]"V" = "l"xx"w"xx""h" [/math] or [math]"V" = "lwh"[/math].

The area of the base of the cardboard box is its length multiplied by its width. So, volume of a rectangular prism can also be calculated by multiplying base times height.

  • [math]"Volume" = "Base" xx"Height"[/math]

This formula is often shorted to: [math]"V" = "b"xx""h" [/math] or [math]"V" = "bh"[/math].

When finding the volume of rectangular prisms it is important to pay attention to the units. Your answers should be in cubic units. For example, if you measured the volume of the cardboard box in feet, your answer would be in cubic feet [math](ft^3)[/math]. Also be sure to check that the units for all three measurements are in the same form. If you measured two sides of the cardboard box in feet and one side in inches, you would need to convert all the units to either feet or inches before finding the volume.


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