NOTE

This document expects a very basic understanding of multiplication and division.

NOTE

This document is meant to be read after the Standards for Distance document. If you have not read that document yet, please do so before continuing.

Standards for Volume

Volume is a measure of how much space an object takes up.

Cubic Meters

The basic unit of volume in the metric system is the cubic meter. A cubic meter is equal to the amount of space taken up by a cube that is 1 meter on each side. This is a very convenient unit of measurement because it is easy to visualize and compare to other objects.

A cubic meter is approximately equal to the volume of a washing machine, or the amount of water that would fill a bathtub. Cubic units are represented with a superscript 3, like this: ${\text{m}}^3$.

Creating Cubic Units

To calculate the volume of an object, you can use the formula:

$$\text{Volume}=\text{Length}\times \text{Width}\times \text{Height}$$

WARNING

The units used in the formula must be the same. For example, if you are using meters, all measurements must be in meters.

For example, if you have a box that is 2 meters long, 1 meter wide, and 0.5 meters tall, you can calculate the volume like this:

$$\text{Volume}=2\times 1\times 0.5=1\text{ cubic meter}$$

Metric Prefixes

NOTE

"Taking the cube" of a number means multiplying it by itself three times. For example, the cube of 3 is $3\times 3\times 3=27$.

Just like with distance, we can use metric prefixes to make it easier to work with very large or very small volumes. However, the conversion factors are a little different.

To convert between different units marked as "cubic", you must take the cube of the conversion factor. For example, to convert 5 cubic kilometers to cubic meters, you would multiply by 1,000,000,000 (since 1,000 cubed is 1,000,000,000).

As an example, let's convert 10 cubic millimeters to cubic centimeters. Since 1 millimeter is 0.1 centimeters, the conversion factor is 0.1.

If this were a linear (non-cubic) measurement, you would divide by 0.1. However, since this is a cubic measurement, you must take the cube of 0.1, which is 0.001.

So, to convert 10 cubic millimeters to cubic centimeters, you would multiply by 0.001:

$$10{\text{ mm}}^3\times 0.001=0.01{\text{ cm}}^3$$

It is normal to not understand or be confused by this at first. It is a complex concept that takes time to understand. If you are having trouble, please ask for help.

Liters

The liter is another common unit of volume that is used in everyday life. A liter is equal to 1,000 cubic centimeters, or 1 cubic decimeter. It avoids the need for cubic units, which can be difficult to work with.

A liter is approximately equal to the volume of a small bottle of soda. Liters are represented with a lowercase l or a capital L.

Converting Between Cubic Meters and Liters

To convert between cubic meters and liters, you can use the conversion factor 1,000. This is because there are 1,000 liters in a cubic meter.

For example, to convert 5 cubic meters to liters, you would multiply by 1,000:

$$5{\text{ m}}^3\times 1,000=5,000\text{ L}$$

To convert 10 liters to cubic meters, you would divide by 1,000:

$$10\text{ L}÷1,000=0.01{\text{ m}}^3$$

Liter Examples

Some example sizes:

• A large bottle of soda is around 2 liters.
• A large pot is about 10 liters.
• The entire volume of a human body is about 70 liters.
• A small swimming pool is about 50,000 liters.
• The entire volume of the Earth's oceans is about 1,332,000,000,000,000,000,000 liters (or 1.332 billion cubic kilometers, $1.332\times {10}^9$ km${}^3$).
• A regular, adult human body is about 70 liters.

Metric Prefixes

Just like with cubic meters, you can use metric prefixes to make it easier to work with very large or very small volumes. The conversion factors are the same as with standard, linear measurements.

For example, to convert 5 kiloliters to liters, you would multiply by 1,000:

$$5\text{ kL}\times 1,000=5,000\text{ L}$$

Other Units

Other units of volume exist, such as the gallon, the pint, and the cup. These units are generally outdated and not used in scientific contexts. However, they are still used in some countries, such as the United States.

Rough conversions between some of these units and liters are as follows:

• 1 gallon is about 3.785 liters. (US)
• 1 gallon is about 4.546 liters. (UK)
• 1 pint is about 0.568 liters. (UK)
• 1 pint is about 0.473 liters. (US)
• 1 cup is about 0.24 liters.

More units exist. You may find it useful to research these units if you are interested in learning more.