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 4
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