Question

Twenty seven solid iron spheres, each of radius $r$ and surface area $S$ are melted to form a sphere with surface area $S^{\prime }$. Find the radius $r^{\prime }$ of the new sphere,

Answer 1

Given the radius of the small iron sphere is $r$ and the radius of the new sphere is $r^{\prime }$.

Then according to the problem

$27\times \frac{4}{3}\times r^3=\frac{4}{3}\times r^{\prime 3}$

or, $27r^3=r^{\prime 3}$

or, $r^{\prime }=3r$.