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
Solve the following problems. The answers are here.
- Convert 16 m3 to kL.
- How many cL will fit in a box with a volume of 38.2 Mm3?
- How many liters will fit into a box that measures 2.3 m x 1.8 m x 4.0 m?