Unit Conversions B

Introduction What happens if you need to convert an area, or volume, into different units. A problem comes up, but there is a simple trick to get out of it. Let me illustrate with an example:

Example Let's say you need to calculate the area of a standard U.S. letter-size sheet of paper, 8.5 by 11 inches. The area of a rectangle is (length x width), of course.

Oops! You were supposed to calculate that in square centimeters, not square inches. Let's try converting. As you know, 2.54 cm equals one inch.

That's not going to work, because you have inch² on 'top', and only inch on the 'bottom'. The units don't "cancel" properly.

So what's the way out of this conundrum? Square the entire conversion factor! (Remember, that whole fraction in parentheses is equal to the number 1, so after squaring it is still equal to 1.)

Do this calculation yourself, as practice.

If you need to convert volume units use the same trick, except you cube the conversion factor instead of squaring it.

Example The average volume of an adult human brain is about 1450 cubic centimeters. What is that in cubic inches?

Additional Activities & Practice

1. The volume of water in Earth's oceans is about 1.3 billion cubic kilometers. What is that in cubic miles? (NOTE: 1 mile = 1.609 km)

2. An adult human bladder can hold about 500 cubic centimeters of urine. How many cubic inches is that?

3. The area of Earth's land surface is about 150 million square kilometers. What is the area in square miles?

4. How many square feet are in one square mile? (There are 5280 feet in a mile.)

5. An acre is a unit of area, equal to the area of a rectangle that is 66 by 660 feet. (a) How many square feet is an acre? (b) How many square furlongs is that? (c) How many square meters?

6. The acre-foot is a unit of volume that gets used by water resource managers in the U.S., used to describe the capacity of reservoirs, for example. How many cubic meters is equal to one acre-foot?