Math Homework Help: Volume and Capacity

Understanding Volume and Capacity

The volume of a solid object is the amount of space that it takes up. Capacity is the volume of liquid or any other substance that a container can hold. You can think of volume as the space something fills up, while capacity is the amount of space that's available to be filled up. Things that have volume include solid objects, like rocks and trees. Liquids, like water, juice and milk, also have volume. In contrast, empty boxes, buckets and bottles have capacity.

Measuring the Volume of Solids

The volume of a solid object is calculated by multiplying the area of its base by its height (V = b x h). It's reported in cubic units, like cubic centimeters, cubic meters and cubic inches. The type of cubic units that you use to report an object's volume depends on the type of units that its base and height are measured in. For instance, if a brick has a base with an area of ten square inches and a height of eight inches, its volume would be 80 cubic inches (10 x 8 = 80).

Liquid Volume

The volume of liquids is usually measured in units like liters, milliliters, gallons or pints. These units are only used for volume, so you don't need to add the word 'cubic' to the units in your answer. The volume of a liquid is typically calculated by determining the capacity of its container.

Finding the Capacity

Since containers generally hold liquids or loose substances, their capacities are usually measured in units of liquid volume (quarts, liters and so on). Containers, like measuring cups and beakers, have their capacities marked on the side, and you can measure the volume of a quantity of liquid by placing the container on a level surface and filling it to the point that's marked.

If a container's capacity isn't indicated, you can calculate it by figuring out what its volume would be if it were full. Here are two ways to do this:

1. Fill the container with water, and then measure the liquid needed to fill it in a beaker or measuring cup. The volume of liquid that the container can hold is equal to its capacity.
2. Measure the inside dimensions of the container, and use the appropriate formula to calculate its cubic volume. Convert the answer into cubic decimeters (10 cubic decimeters = 1 cubic meter), and then convert that answer into liters (1 cubic decimeter = 1 liter).