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
To see how an area changes, write its formula and put the changed measurement into it.
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 is proportional to the height: with height \(2h\) it becomes \(2\pi r(2h)=2\times2\pi rh\).
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 \(3\pi r^2\), proportional to the square of the radius: with radius \(2r\) it becomes \(3\pi(2r)^2=12\pi r^2=4\times3\pi r^2\).