In this activity, we will find the volume of compound 3D shapes.

 

You may need a calculator for this activity.

 

What does a compound 3D shape look like?

It is made up of different 3D shapes.

 

Here is an example:

 

 

In this case the shape is made up of two cuboids.

It also forms an L-shaped prism.

 

Volume of a prism = Area of cross section x length

 

This means that if we can find the area of the cross section (an L shape), we can multiply it by the length to get the volume.

 

 

Let's try one:

 

Example

Calculate the volume of the 3D shape.

 

 

Answer

1) Area of the cross-section:

 

 

Split rhe L shape into two rectangles and calculate the area of each:

 

 

Area A =  5 x 2  = 10 cm²

Area B = 3 x 3 = 9 cm²

Total area of L = 10 + 9 = 19 cm²

 

2) Multiply the cross-section x length

Volume = 19 x 7

Volume = 133 cm³

 

Note - The volume is 3D so the units are cm³