Question

An iron spherical ball of radius 21cm is melted and it is re-casted in 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 $\frac{4}{3}\pi R^3=x\frac{2}{3}\pi r^3$

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

$\Rightarrow \frac{4}{3}\pi {\left(21\right)}^3=x\frac{2}{3}\pi {\left(7\right)}^3$

$\Rightarrow x=\frac{2\times 21\times 21\times 21}{7\times 7\times 7}$
$\Rightarrow x=54$