Consider the following statements:

I. If the height of a cylinder is doubled, the area of the curved surface is doubled.
II. If the radius of a hemispherical solid is doubled, its total surface area becomes fourfold.

Which of the above statement(s) is/are true:

Both I & II

The correct answer is Option (4) → Both I & II

Let’s evaluate both statements one by one.

Statement I

Curved surface area (CSA) of a cylinder:

$\text{CSA} = 2\pi r h$

If height h is doubled:

$\text{New CSA} = 2\pi r (2h) = 2(2\pi r h)$

So, the curved surface area becomes doubled.

Statement I is true

Statement II

Total surface area (TSA) of a hemisphere:

$\text{TSA} = 3\pi r^2$

If radius r is doubled:

$\text{New TSA} = 3\pi (2r)^2 = 3\pi \cdot 4r^2 = 4(3\pi r^2)$

So, the total surface area becomes four times.

Statement II is true

Correct answer: Both I & II