Calculate Volumes of Compound 3D Shapes

In this activity, we will be using what we know about the volume of cubes and cuboids to calculate the volume of compound shapes.

Volume of Cube

Volume = width x height x depth (these are all the same in a cube)

Volume of Cuboid

Volume = width x height x depth

Let's have a look at a compound shape.

We can see it is made up of a large cuboid with a hole, which is a small cuboid!

Like this:

To find the volume of the shape, we can find the volume of the large cuboid and the volume of the hole (also a cuboid).

Then subtract to get the C-shaped prism.

Volume = Large volume - small (hole) volume

Let's try a question!

Example

Calculate the volume of the compound shape.

Answer

volume of compound shape = volume of large cuboid - volume of small (hole) cuboid

The large cuboid  = 5 x 6 x 10 = 300 cm³

The smaller cut-out cuboid = 3 x 7 x 6 = 126 cm³

So, the volume of the compound shape = 300 - 126  = 174 cm³

Let's have a go at some questions now!