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4.Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will be needed to form a cube?
Answer :

Given, the sides of the cuboid as 5 cm, 2 cm and 5 cm.

So we have the volume of the cuboid =\( 5 cm \times 2 cm \times 5 cm = 50 cm^3\)

We have the prime factors of 50 as:

\(50 = 2 \times 5 \times 5\)

To make it a perfect cube, we must have \(2 \times 2 \times 2 \times 5 \times 5 \times 5\)

\(\Rightarrow 20 \times (2 \times 5 \times 5)\)

\(\Rightarrow 20 \times volume \;of \;the\; given \;cuboid\)

Thus,we have the required number of cuboids = 20.