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Question

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


Solution

Given,
Dimensions of the cuboid $$=49 \, cm \times 33\, cm \times 24 \,cm$$
When a solid is converted from one form to another, the amount of volume remains same.
Volume of cuboid $$=$$ Volume of sphere
$$\Rightarrow \quad\displaystyle 49\times 33\times 24=\frac{4}{3} \pi r^3\\$$
$$\Rightarrow \quad{r}^3 = \dfrac{49\times 33\times 24\times 3\times 7}{4\times 22}$$
$$ \Rightarrow \quad {r}^{3}=49\times 27\times 7$$
 $$\Rightarrow \quad r= 21\,cm$$
Hence, the radius of sphere is $$21\ cm$$

Mathematics

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