The image below shows a rectangular prism with length 5 units, width 3 units, and height 2 units. Notice that the length of each edge corresponds to the number of unit cubes that could be lined up side by side along that edge.
We can find the number of unit cubes that could fit inside the rectangular prism by taking the product of the three side lengths. This gives 5\times3\times2=30, so there are 30 unit cubes in the prism, which means it has a volume of 30\text{ unit}^3.
In the same way that the area of a two dimensional shape is related to the product of two perpendicular lengths, the volume of a three dimensional shape is related to the product of three mutually perpendicular lengths (each of the three lengths is perpendicular to the other two).
A cube can be thought of as a special type of rectangular prism, one that has all sides equal in length. The formula for the volume of a cube is similar to the formula for the area of a square.
Find the volume of the rectangular prism shown.
A box of cereal is in the shape of a rectangular prism. It measures 24 cm by 12 cm by 19 cm.
What is the volume of the box of cereal?
The company that makes these cereal boxes also makes a jumbo size box, which is twice as long, twice as wide, and twice as tall as the regular size boxes. What is the volume of the jumbo box of cereal?
The volume of the rectangular prism is given by:
The volume of the cube is given by:
Once we are familiar with finding the volume of rectangular prisms and cubes, the same idea can be used to determine the volume of more complicated shapes. If we think of a composite shape as being built out of a number of smaller, simpler shapes, then the volume of the composite shape is the sum of the volume of each shape it is built from.
This complicated shape is built from simple rectangular prisms.
Depending on the configuration of the composite shape, it may be useful to think of building it from a large rectangular prism that then has smaller volumes taken away.
Find the volume of the composite solid shown by breaking it up into rectangular prisms.
The volume of a composite shape is the sum of the volume of each shape it is built from.
Depending on the configuration of the composite shape, it may be useful to think of building it from a large rectangular prism that has smaller volumes taken away.