Question

The radii of the internal and external surfaces of a metallic spherical shell are $3cm$ and $5cm$ respectively. It is melted and recast into a solid right circular cylinder of height $10\frac{2}{3}cm$. Find the diameter of the base of the cylinder.

Answer 1

Let the radius of the base of the cylinder be $r$ cm.

Then volume of the metallic solid cylinder of height $10\frac{2}{3}cm$
= volume of the metal in the spherical shell

$\Rightarrow \pi \times r^2\times \frac{32}{3}=\frac{4}{3}\pi (5^3-3^3)$

$\Rightarrow \frac{32}{3}{r}^2=\frac{4}{3}(125-27)$

$\Rightarrow r^2=\frac{3}{32}\times \frac{4}{3}\times 98\Rightarrow r^2=\frac{49}{4}\Rightarrow r=\frac{7}{2}cm$

$\Rightarrow r=\frac{7}{2}cm$

$\Rightarrow D=7cm$