Answer: Option A
Let,
$$\eqalign{
& OP = OQ = OR = r \cr
& \therefore OR = h = r \cr} $$
∴ Curved surface area of the hemisphere = $$2\pi {r^2}$$
Curved surface area of a cone = $$\pi rl$$
Where,
$$\eqalign{
& l = \sqrt {{h^2} + {r^2}} \cr
& \,\,\,\,\, = \sqrt {{r^2} + {r^2}} \cr
& \,\,\,\,\, = r\sqrt 2 \cr} $$
∴ Required ratio :
$$\eqalign{
& = \frac{{2\pi {r^2}}}{{\pi rl}} \cr
& = \frac{{2\pi {r^2}}}{{\pi r \times r\sqrt 2 }} \cr
& = \frac{2}{{\sqrt 2 }} \cr
& = \frac{{2 \times \sqrt 2 }}{{\sqrt 2 \times \sqrt 2 }} \cr
& = \frac{{2\sqrt 2 }}{2} \cr
& = \frac{{\sqrt 2 }}{1}\,Or\,\sqrt 2 :1 \cr} $$