# Units of Conversion: Cubic (Volume) Measure

Basic to the understanding of unit conversion is the understanding of equivalence, the understanding of the multiplicative identity of 1, and how the two are related. For a review of these concepts, click on Review.

You will also need to multiply and reduce fractions. If you have forgotten how to manipulate fractions, visit Fractions for Adults on SOSMath for an in-depth review.

Review the following table of Standard Units of Conversion to see if you can create fractions that have a value of 1. You can click to examples following each table.

Cubic Measure

Example 4: Find the volume of a building that is 100 rods by 200 meters at the base and is 3 decameter high. Give your answer in feet.

Solution:

Note: The volume of the building is found by multiplying the area of the base of the building by the height of the building.

You cannot multiply different units. For example 200 rods x 200 meters has no meaning.

The first step, therefore, is to convert the three dimensions of the building to one unit.

Since the answer is to be in feet, let's convert all the dimensions to feet.

• According to the linear conversion table, 1 rod is equivalent to 16.5 feet. Therefore, the fraction is equivalent to 1.
• 100 rods can be written x 1 which in turn can be written x This is simplified to 1,650 feet.
• According to the linear conversion table, 1 meter is equivalent to 3.2808 feet. Therefore, the fraction is equivalent to 1.
• 200 meters can be written x 1 which in turn can be written x This is simplified to 656.16 feet.
• According to the linear conversion table, 1 decameter is equivalent to 328.083 feet. Therefore, the fraction is equivalent to 1.
• 3 decameters can be written x 1 which in turn can be written x This is simplified to 984.249 feet.
• The volume of the building using the original dimensions is 100 rods x 200 meters x 3 decameters.
• The volume of the building using the equivalent dimensions is

If you would like to work some problems click on Problems.

[Units of Conversion]