Parikshit makes a cuboid of plasticine of sides $ 5 \mathrm{~cm}, 2 \mathrm{~cm}, 5 \mathrm{~cm} $. How many such cuboids will he need to form a cube?

Given :

Parikshit makes a cuboid of plasticine of sides \( 5 \mathrm{~cm}, 2 \mathrm{~cm}, 5 \mathrm{~cm} \).

To find :

We have to find the number of cuboids required to form a cube.

Solution :

Volume of a cuboid of height $h$, length $l$ and breadth $b$ is $lbh$.

This implies,

Volume of the given cuboid $= 5\ cm\times2\ cm\times5\ cm = 50\ cm^3$.

The minimum length required to form a cube $=$ LCM of 5, 2 and 5 $=5\times2=10$.

Therefore,

Minimum length required to form a cube $= 10\ cm$.

Volume of the cube so formed $= (10\ cm)^3=1000\ cm^3$.

Number of such cuboids required $= \frac{1000}{50}=20$ . 

Therefore, 20 such cuboids are required to form a cube.

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Updated on: 10-Oct-2022

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