Squares and Cubes

When converting units that involve squares and cubes it is important to remember:

The superscript applies to the unit, NOT to the number

But, you must also remember that an exponent OUTSIDE of parentheses applies to EVERYTHING inside the parentheses.

There are several ways to approach problems that contain squares and cubes, but the most straightforward is to first pretend that the unit is not squared (or cubed) and set up the problem that way. Then, square (or cube) the conversion factors (the whole factor, not just the unit).

Sample Problem 1

A block has a surface area of 13.9 m². What is the area in cm²?

Sample Problem 2

A doctor orders that her patient gets 25 cm³ (sometimes called cc's - for cubic centimeters) of a certain medicine. How many m³ is that?

Your turn

Solve the following problems involving units that are squared or cubed. The answers are here.

1. How many km² are in 357 mm²?
2. A container holds 0.500 m³ of liquid. How many km³ could it hold?
3. Convert 34.9 km³ to µm³.

Back to Factor Label Problems

on to Cubic Length and Volume