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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?

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.