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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