Here’s an example problem for finding volume using unit cubes.

Find the volume of the following shape:

To solve, count the number of cubes in one layer of the shape. Some people find it easier to count the cubes in the front layer while other people find it easier to count the cubes in the bottom layer. Both ways will give the same answer, so it’s up to you. Just for fun, we’ll complete this problem both ways. First, let’s count the cubes in the front layer.

The front layer of our shape is 12 cubes wide and 6 cubes tall. If we multiply 12 by 6 we’ll see that there are 72 cubes in the front layer.

Since there are 3 layers of 72 cubes we just need to multiply 72 by 3 to find our answer.
72 x 3= 216
The volume of our shape is 216 cubic units.

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Now let’s complete the same problem by first counting the amount of cubes in the bottom layer.

The bottom layer of our shape is 12 cubes wide and 3 cubes deep. If we multiply 12 by 6 we’ll see that there are 36 cubes in the bottom layer.

Since there are 6 layers of 36 cubes we just need to multiply 36 by 6 to find our answer.
36 x 6= 216
The volume of our shape is 216 cubic units.

Some of the problems in our worksheets include composite figures. You’ll need to be able to break down the figures into smaller 3D shapes, find the volume of each piece, and then add the numbers together. If you’re having trouble visualizing how these shapes break down, you may want to practice more with simple rectangular prisms like the one above.

You can also use colored pencils to shade the pictures, like we did in the example.