Consider the following statements, which of them is/are correct?
A. If the height of cylinder is doubled, the area of curved surface is doubled.
B. If the radius of a hemispherical solid is doubled, its total surface area becomes fourfold.
C. If a hemisphere and cone have equal bases and equal heights, then the ratio of curved surface area is $$\sqrt{2}:1$$.

Let's analyse the statements.

Statement A:

Curved surface area of cylinder is given by the formula $$2\pi\ rh$$, where r is the radius of the base of cylinder and h is height

So, we can see in this area is directly proportional to height

So, if height is doubled, area will be doubled

So, statement A is correct.

Statement B:

Total surface area of hemisphere is given by the formula $$3\pi\ r^2$$

So, if radius is doubled, total surface area will become 4 times

So, statement B is also correct.

Statement C:

Let say the radius be r and height be h for both hemisphere and cone

So, curved surface area of cone = $$\pi\ rl$$ = $$\pi\ r\sqrt{\ r^2+h^2}$$

curved surface area of hemisphere = $$2\pi\ r^2$$

So, required ratio is = $$\dfrac{2\pi\ r^2}{\pi\ r\sqrt{\ r^2+h^2}}=\dfrac{2r}{\sqrt{\ r^2+h^2}}$$

From this we can't get a definite numerical value of ratio

So, statement C is wrong.

So, correct answer is option C.