Question

A solid piece of iron in the form of a cuboid of dimension $49cm\times 33cm\times 24cm$ is melted to form a solid sphere. Find the radius of the sphere.

Answer 1

Given,

Dimensions of the cuboid $=49cm\times 33cm\times 24cm$

When a solid is converted from one form to another, the amount of volume remains same.

Volume of cuboid $=$ Volume of sphere

$\Rightarrow 49\times 33\times 24=\frac{4}{3}\pi r^3$

$\Rightarrow r^3=\frac{49\times 33\times 24\times 3\times 7}{4\times 22}$

$\Rightarrow r^3=49\times 27\times 7$

$\Rightarrow r=21cm$

Hence, the radius of sphere is $21cm$