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
Doubling a length doubles an area in which that length appears once, and makes four times an area in which it appears squared. So each statement is checked by looking at its formula.
I. If the height of a cylinder is doubled, the area of the curved surface is doubled. Correct. The curved surface area is \(2\pi rh\), which has the height \(h\) to the first power:
New curved surface area \(=2\pi r(2h)=2\times2\pi rh\), twice the old one
II. If the radius of a hemispherical solid is doubled, its total surface area becomes fourfold. Correct. A solid hemisphere has a curved surface \(2\pi r^2\) and a flat circular base \(\pi r^2\), so its total surface area is \(3\pi r^2\), with the radius squared:
New total surface area \(=3\pi(2r)^2=4\times3\pi r^2\), four times the old one