Question

An iron spherical ball of radius 21cm is melted and re-casted into hemispheres of radius 7cm. The number of balls formed will be

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Answer 1

The volume will remain constant.

Let's assume $x$ such hemispherical balls will be formed.

So $\frac{4}{3}$ $\pi$ $R^3=x\times$ $\frac{2}{3}$ $\pi$ $r^3$

(Where R is the radius of spherical ball and r is the radius of hemisphere)

$\Rightarrow \frac{4}{3}$ $\pi$ ${21}^3=x\times$ $\frac{2}{3}$ $\pi$ $7^3$

$\Rightarrow x=54$