Question

The diameters of internal and external surfaces of a hollow spherical shell are $10cm$ and $6cm$ respectively. If it is melted and recast into a solid cylinder of length of $2\frac{2}{3}cm$, find the diameter of the cylinder.

Answer 1

Volume of sphere = $V_s=\frac{4}{3}\pi (R_e^3-R_i^3)$

$V_s=\pi r^2\left(\frac{8}{3}\right)$

$\Rightarrow r=\sqrt{\frac{4(5^3-3^3)}{8}}=7cm$

So the diameter $=14$ cm