Practice Problem 4

Calculate the volume in liters of a cubic container 0.500 meter tall.

Solution

We can start by calculating the volume of the container in units of cubic meters, which is the product of its height times its length times it width.

V = (0.500 m x 0.500 m x 0.500 m) = 0.125 m3

It isn't always obvious what should be done next, so let's look at the goal of the calculation and work backwards.

Our goal is the volume of the container in liters. We might therefore ask: What do we know about this unit? We know that a liter contains 1000 mL. But a milliliter is equivalent to a cubic centimeter. Thus, 1 liter contains 1000 cubic centimeters.

1 L = 1000 cm3

If we can convert the volume of the container from cubic meters to cubic centimeters, we can then convert cubic centimeters to liters. The conversion between cubic meters and cubic centimeters is based on the following equality.

1 m = 100 cm

The unit factor used to do this conversion must be cubed, however, because we have to convert from cubic meters to cubic centimeters.

Now that we know the volume in cubic centimeters, we can calculate the volume in liters.