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:

I & II Both

The correct answer is Option (3) → I & II Both

Let’s check each statement one by one.

Statement I

Curved surface area (CSA) of a cylinder

$\text{CSA} = 2\pi rh$

If height h is doubled:

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

So, the curved surface area doubles.
Statement I is true

Statement II

Total surface area (TSA) of a hemispherical solid

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

If radius r is doubled:

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

So, the total surface area becomes four times.
Statement II is true

Correct answer: I & II Both