A sphere of maximum volume is cut out from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut out sphere is :

Answer: Option B

Volume of hemisphere = $$\frac{2}{3}\pi r^3$$
Volume of biggest sphere :
= Volume of sphere with diameter r
$$\begin{array}{rl}& =\frac{4}{3}\pi {\left(\frac{r}{2}\right)}^3\\ & =\frac{1}{6}\pi r^3\end{array}$$
∴ Required ratio :
$$\begin{array}{rl}& =\frac{\frac{2}{3}\pi r^3}{\frac{1}{6}\pi r^3}\\ & =\frac{4}{1}i.e.,4:1\end{array}$$