Relating cubic length and volume

The units of volume in the metric system are actually defined based on length. So a mL is defined as the volume of a box that measures 1 cm on each side. In other words, imagine making a little, perfectly square box, where each side is one centimeter long. If you filled that box with water, it would hold exactly one milliliter.

What that means mathematically is

As a result of this connection between volume and cubic length, we can convert between cubed length units and non-cubed volume units.

If you start with a cubed unit, you will first convert to cm³, and then use the first fraction above to change into volume units.

If you start with a volume unit you will first convert it to mL, and then use the second fraction above to change into cubed units.

Sample Problem 1

How many L of water will fit in a plastic container that has a volume of 3.92 m³?

Sample Problem 2

Convert 49.3 cL to mm³

Your Turn

Solve the following problems. The answers are here.

1. Convert 16 m³ to kL.
2. How many cL will fit in a box with a volume of 38.2 Mm³?
3. How many liters will fit into a box that measures 2.3 m x 1.8 m x 4.0 m?

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