A cylinder, a Hemi-sphere and a cone stand on the same base and have the same heights. The ratio of the areas of their curved surface is:

The cylinder, hemisphere and cone stand on the same base and have the same height. Let the radius of the three solids be $$r$$ and the height be $$h$$.

Height of the hemisphere, $$h$$ = $$r$$ (Radius)

Curved surface area of the cylinder = $$2*\pi*r*r$$ = $$2*\pi*r^2$$
Curved surface area of the hemisphere = $$2*\pi*r^2$$
Curved surface area of the cone = $$\pi*r*\sqrt{r^2+r^2}$$ = $$\pi*r*\sqrt{r^2+r^2}$$ = $$\pi*r^2*\sqrt{2}$$
Ratio = $$2:2:\sqrt{2}$$ = $$\sqrt{2}:\sqrt{2}:1$$
As the answer is not among the given options, option D is the right answer.