Understand Volumes of Cubes, Cuboids and Compound Figures

Look at the compound figure below.

Think of it as a large cuboid with the dimensions a x b x d with a smaller cuboid of dimensions b x c x b cut out.

a = 10 cm

b = 4 cm

c = 2 cm

d = 6 cm

How would you calculate the volume?   

We would need to find the volume of the large cuboid first and then subtract the volume of the small cut-out cuboid shape.

The large cuboid  has lengths a, b and d, which is 10 x 4 x 6.

10 x 4 x 6 = 240

The smaller cut-out cuboid shape has lengths b, c and b again, which is 4 x 2 x 4

4 x 2 x 4 = 32

So the volume of the shape above is 240 - 32 = 208 cm³

Let's have a go at some questions now.