Question

How many cuboids of size 15 cm × 30 cm × 15 cm to make a perfect cube of side 30 cm?

• A. 4
• B. 5
• C. 6
• D. 7

Answer 1

The correct option is A 4

Volume of given cuboid is 15 × 30 × 15 = 6750 $c{m}^3$.
Using the prime factorisation method,
6750 = 2 × 3 × 3 × 3 × 5 × 5 × 5
If 2 × 2 is multiplied in the given factors, we get a perfect cube root as each prime factor appears 3 times.
That means 6750 × 2 × 2 = 27000 = 30 × 30 × 30
So, four such cuboids are required to get a cube of side 30 cm.