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## Question

primary 6 | Maths
| Measurement

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Hi need help

= 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.

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