Resource: Volume and Shapes

The objects we encounter in our everyday lives have different physical properties. Many of these properties, including height and weight, can be measured using common tools. For example, to determine the height of a desk, you might use a tape measure or meter stick. To learn the weight of a phone book, you might place it on a bathroom scale.

Volume is another important physical property that we encounter in our everyday lives. To understand volume, you must first understand matter. Anything that exists is made of matter. Matter occupies space, and volume is the amount of space that matter occupies.

Depending on the shape of an object, measuring its volume can be straightforward or complicated. For objects with a regular shape, such as a phone book or a bowling ball, a simple formula can be applied to calculate volume. But for objects with an irregular shape, such as a pear or a paper clip, volume must be calculated in other ways. One method, called water displacement, involves placing an object in a marked container of water and measuring how much the object raises the water level when it is completely submerged. By knowing how much water is "displaced" by the object, you can determine how much space it takes up.

The volume of an object, like the various cube configurations featured in this video segment, is equal to the combined volume of its parts. That is, if ten cubes of the same size are attached to one another, then the volume of the assembled object—no matter what its overall shape—is equal to the sum of the volume of all ten cubes.

• Is the volume of an object always the same as the volume of the pieces that make it up?
• Can you think of a shape that would have a volume greater than the volume of the pieces that make it up? A volume less than the volume of its pieces?
• If you weighed each of the different shapes you can make with a set of blocks, how do you think the weights would compare?
• If you have six cubes that are all the same, how many different shapes can you make? Do you think the different shapes take up the same or different amounts of space?