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:
Answer & explanation
Correct answer: option 3
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