The capacities of two hemispherical vessels are 6.4 litres and 21.6 litres. The areas of inner curved surfaces of the vessels will be in the ratio of :

Answer: Option C

Let their radii be R and r
Then,
$$\begin{array}{rl}& \frac{\frac{2}{3}\pi R^3}{\frac{2}{3}\pi r^3}=\frac{6.4}{21.6}\\ & \Rightarrow {\left(\frac{R}{r}\right)}^3=\frac{8}{27}\\ & \Rightarrow {\left(\frac{R}{r}\right)}^3={\left(\frac{2}{3}\right)}^3\\ & \Rightarrow \frac{R}{r}=\frac{2}{3}\end{array}$$
∴ Ratio of curved surface area :
$$=\frac{2\pi R^2}{2\pi r^2}={\left(\frac{R}{r}\right)}^2=\frac{4}{9}or4:9$$