Just like you did with units of length, you can use dimensional analysis to convert units of capacity and volume. As mentioned in the first section of this lesson, medicine and science are two of the primary reasons that the United States must convert between the two systems of measure. This is especially true for volume and capacity.

To move forward with conversions, let’s first review customary and metric units of volume and capacity.

Copy the table below into your notes.

Fill in the chart below for customary units. Click on the blanks to check your answers.

Copy the table below into your notesl.

Fill in the chart below for metric units. Click on the blanks to check your answers.

In the metric system, the most basic unit of volume is the liter. However, the liter is technically not an SI unit of measure, but it is considered to be a metric unit. The SI system uses cubic meters as a unit of volume, and a liter is defined as 1000 cubic centimeters. SI prefixes, such as milli- and kilo- are commonly used with liters. In medicine, a common metric/SI unit of volume or capacity is the cubic centimeter, or cc.

The fluid ounce in the customary system is the smallest unit, but this fluid ounce is much different than the ounce used in measuring weight. This is due to the fact that the fluid ounce measures volume, which refers to the amount of space a given object displaces, whereas the ounce simply measures weight.

Once again, just as 1 inch = 2.54 centimeters was the key in converting between the two systems, the conversion factor you must know for volume and capacity is that 1 fluid ounce (fl. oz.) = 29.6 milliliters (mL) or 1 fluid ounce (fl. oz.) = 29.6 cubic centimeters (cc).

Consider the following problem situation.

Raul reads that the human body contains about 5.6 liters of blood. About how many quarts of blood does the human body contain?

First, make a plan for converting the units from liters to quarts.

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First, you will change liters to cubic centimeters and then cubic centimeters into fluid ounces. From ounces, you will convert to cups and finally convert cups to quarts.

Click on the image below to access the applet. Use the applet to use dimensional analysis in order to perform the conversion.

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Need additional directions?

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Pause and Reflect

How is converting units of capacity or volume with dimensional analysis similar to converting units of length?

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The procedure of dimensional analysis is the same for units of capacity or volume and units of length. Write conversion factors as unit rates, and make sure that units are arranged so that the unit in the denominator will cancel with the unit in the numerator.

Practice

1. Susie's grandmother has a recipe for oatmeal cookies that calls for 21 over 2 1 2 cups of heavy cream, but Susie has a 0.5 liter container of heavy cream. Does she have enough heavy cream to complete the recipe?
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   Need a hint?

   Use dimensional analysis to convert 21 over 2 1 2 cups to fluid ounces, fluid ounces to milliliters, and milliliters to liters. Use the conversion factors provided in the lesson to help you set up your unit rates.
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   The recipe calls for 0.592 liters of heavy cream, but the container only holds 0.5 liters. Susie does not have enough heavy cream to complete the recipe.
2. Dashon and his family are on vacation in Canada. Gasoline costs $1.45 in United States dollars per liter, and the family car’s gasoline tank will hold 18.5 gallons of gasoline. How much will it cost Dashon’s family to fill their gasoline tank?
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   Need a hint?

   Use dimensional analysis to convert 18.5 gallons to quarts, quarts to pints, pints to cups, and cups to fluid ounces. Then, convert fluid ounces to milliliters and milliliters to liters. Use the conversion factors provided in the lesson to help you set up your unit rates.
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3. A water tank for a water cleansing system is in the shape of a rectangular prism with the dimensions shown in the figure below.
   
   

   If 1 gallon is equal to 0.134 cubic feet and 1 gallon is equal to 3.785 liters, what is the capacity of the tank in liters?

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   Need a hint?

   Use the volume formula for a rectangular prism, V = Bh, to calculate the volume of the tank in cubic feet. Use dimensional analysis to convert cubic feet to gallons and then gallons to liters.
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