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 3: Convert 31.5 cubic centimeters to cubic feet.

Answer:

Note: One cubic centimeter means 1 centimeter 1 centimeter 1 centimeter. One cubic centimeter also means 1 centimeter³.

• Write 31.5 cubic centimeters as a fraction.

  

• You can see from the above table that there is a link between centimeters and inches and between inches and feet.
• Since 1,000 cubic centimeters is equivalent to 61.023 cubic inches, you can write the fraction

  

  as an equivalent form of 1.

• Since 1,728 cubic inches is equivalent to 1 cubic foot, you can write the fraction

  

  as an equivalent form of 1.

• Note that is equivalent to

  

• Write as

  

• Multiply the fractions.

  

• Rewrite the numerator and denominator.

  

• Rearrange the numerator and denominator.

  

• At this point, you can cancel the centimeters and the inches.The following steps will remind you why you can cancel these terms.

• Rewrite the above fraction as four fractions so that two of the fractions have an equivalent value of 1.

  

• The above can now be written

  

• It can be further simplified to 0.001112 x 1 cubic foot or 0.001112 cubic foot.

At this point, you might argue that what we illustrated is "over kill" of a simple problem.

Keep in mind, that this site is a tutoring/review site. A shorter version of the same problem is shown below.

• Start with

  

• Cancel the centimeters and the inches to have

  

• This in turn can be simplified to 0.001112 cubic foot.

If you would like to review another example, click on Example.

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

If you would like to go back to the table of contents, click on Table of Contents.

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