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

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 :
$$\eqalign{ & = \frac{{{\text{Volume of hemisphere}}}}{{{\text{Volume of cylinder}}}} \cr & = \frac{{\frac{2}{3}\pi {r^3}}}{{\pi {r^2} \times r}} \cr & = \frac{2}{3}\, Or\,2:3 \cr} $$