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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