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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