Question

Amar made a cuboid of thermocol of dimensions 12 cm, 10 cm and 6 cm. How many minimum number of such cuboids will be needed to form a cube?

Answer 1

The volume of the cuboid = 12 cm × 10 cm × 6 cm

= 720 cu cm

The cube is formed by stacking many such cuboids and it will have side lengths which are multiple of 12, 10 and 6.

The smallest such cube will have a side length of LCM of 12, 10 and 6.

LCM of 12, 10 and 6 -

$12=2\times 2\times 310=2\times 56=3\times 2LCM=2\times 2\times 3\times 5=60$

The smallest such cube will have side length of 60 and volume (in cu. cm) of $(60\times 60\times 60)$ cu. cm.

$\therefore$Number of cuboids of volume $(12\times 10\times 6)$ cu. cm that will fit into a cube of volume $(60\times 60\times 60)$ cu cm.

= $\frac{60\times 60\times 60}{12\times 10\times 6}$
= 300 cuboids