Question

A hemispherical bowl of internal and external diameters $6$ cm and $10$ cm is melted into a right circular cylinder of radius $14$ cm. Find the height of the cylinder

Answer 1

Let the internal and external radii of hemisphere be $r$ and $R$ respectively.
Radius of cylinder be $r^{\prime }=14$ cm
$R=\frac{10}{2}=5$cm
$r=\frac{6}{2}=3$ cm
$\therefore$ Volume of hemisphere $=$ Volume of cylinder
$\Rightarrow \frac{2}{3}\times \pi (R^3-r^3)=\pi (r^{\prime }{)}^{2}h$
$\Rightarrow \frac{2}{3}\times 98=196h$
$\Rightarrow h=\frac{2}{3}\times \frac{98}{196}=\frac{1}{3}$ cm $=0.33$cm