The ratio of the volume of a hemisphere and a cylinder circumscribing this hemisphere and having a common base is :

Answer: Option B

Let the radius of the hemisphere be be r cm
Then, radius of the cylinder = r cm
Height of the cylinder = r cm
∴ Required ratio :
$$\begin{array}{rl}& =\frac{\text{Volume of hemisphere}}{\text{Volume of cylinder}}\\ & =\frac{\frac{2}{3}\pi r^3}{\pi r^2\times r}\\ & =\frac{2}{3}Or2:3\end{array}$$