Question

The length, breadth and height of a cuboid are 18 cm, 6 cm and 12 cm respectively. How many such cuboids will be required to make a cube?

• A. 18
• B. 12
• C. 36
• D. 6

Answer 1

The correct option is C

36

Volume of the cuboid = 18 cm x 6 cm x 12 cm

We know that volume of a cube is (edge)³. So, to make a cube, (18 x 6 x 12) should be made as a perfect cube.

18 x 6 x 12
= 2 x 3 x 3 x 2 x 3 x 2 x 2 x 3
= 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3

Making triplets, we find that prime factors 2 and 3 are left out. So, to make it a perfect cube, we need to multiply it by 2 x 2 x 3 x 3 = 36

Thus, 36 x 18 x 6 x 12 = (36)³ = Volume of cube

Thus, the number of cuboids required to make a cube is 36.