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

Solution(By Examveda Team)

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