Length of cuboid B
= 22cm - 11cm
= 11cm

Total volume of the cuboids
= 11 x 4 x 12 + 11 x 4 x 6
= 528 + 264
= 792 cm³

This is equal to the volume of the three cubes combined.

Cubes have all their sides equal length. So V = L x L x L

Since their side lengths are whole numbers, you can try to guess and check.

448-> guess and check:) (took me forever)

its 8x8x8 - 4x4x4

You can start by writing out the volumes of various cubes, each 1cm longer than the previous.

1 x 1 x 1 = 1
2 x 2 x 2 = 8
3 x 3 x 3 = 27
4 x 4 x 4 = 64
5 x 5 x 5 = 125
6 x 6 x 6 = 216
7 x 7 x 7 = 343
8 x 8 x 8 = 512
9 x 9 x 9 = 729

A faster way to guess here is to subtract the volume of the largest cube from 792 and see which two other cubes can sum to this.


792 - 729 = 63
No two other cubes can add up to 63, so the largest cube cannot be 9 x 9 x 9

Now try subtracting the volume of the next largest cube, 512.

792 - 512 = 280

This can be obtained by adding 64 and 216.

So the correct combination is :

4 x 4 x 4 + 6 x 6 x 6 + 8 x 8 x 8

Difference in volume of the smallest and largest cubes = 512 - 64
= 448 cm³