Video and Examples

Learn how to find the volume of rectangular prisms.

Rectangular prisms

Volume is the amount of space inside a 3-dimensional figure. It is measured in cubic units. A cubic centimeter is a cube that is 1 cm wide, 1 cm long, and 1 cm high.

Another way to think of volume is to find the number of unit cubes necessary for building the figure.

Example 1

Suppose this is a cubic unit:

How many cubic units would be needed to build this object?

Example 2

How many unit cubes are needed to build this object?

 Example 3 How many cubes are in this figure? [show answer]   There are 6 cubes on the bottom "floor" There are also 6 cubes on the second "floor" And there are 6 cubes on the third (top) "floor" So, there are 18 cubes in this figure.

Example 3 shows us that a shortcut for finding the volume of a rectangular prism is to find the number of cubes on the bottom "floor" and the multiply by the number of floors.

 Volume = (number of cubes on the bottom floor) x (number of floors) Volume = Area of the base x height Volume = l • w • h

Let's practice this shortcut with a few more examples...

 Example 4 Find the volume of this rectangular prism. Volume = (Area of the base) • (height) Volume = (4 • 3) • 5 Volume = 60 $\mbox{cm}^3$ (If you look at each layer, there are 12 cubes in each. There are 5 layers, so that would make a total of 60 cubes.)

 Example 5 Find the volume. [show answer]   Volume = l • w • h Volume = 6 • 3 • 3 Volume = 36 cubic units

 Example 6 Find the volume. [show answer]   V = l • w • h V = 5 • 4 • 7 V = 140 units cubed

Self-Check

 Question 1 Find the volume of this prism. [show answer]   $\large~24\mbox{ u}^3$

 Question 2 Find the volume. [show answer]   $\large~42\mbox{ cm}^3$

 Question 3 Find the volume. [show answer]   $\large~48\mbox{ cm}^3$