A sphere and a hemisphere have the same volume. The ratio of their curved surface area is:

Answer: Option D

Let the radius of hemisphere and sphere be 'r' and 'R'
$$\begin{array}{rl}& \Rightarrow \frac{4}{3}\pi R^3=\frac{2}{3}\pi r^3\\ & \frac{R^3}{r^3}=\frac{1}{2}\\ & \frac{R}{r}=\frac{1}{\text{root}3\text{of}2}\\ & \Rightarrow \text{Ratio of curved surface area}\\ & =\frac{4\pi R^2}{2\pi r^2}\\ & =\frac{2R^2}{r^2}\\ & =\frac{2\times 1}{{\left(\text{root}3\text{of}2\right)}^2}\\ & =\frac{2}{{\left(2\right)}^{\frac{2}{3}}}\\ & \Rightarrow \frac{R}{r}=\frac{2^{\frac{1}{3}}}{1}\end{array}$$