Question:
If the radius of a cylinder is tripled but its curved surface area is unchanged, then its height will be
(a) tripled
(b) constant
(c) one sixth
(d) one third
Solution:
The correct answer is option (d) one third
Explanation:
We know that the curved surface area of a cylinder is 2πrh, when the radius is “r” and height is “h”.
Let “H” be the new height.
When the radius of a cylinder is tripled, then the CSA of a cylinder becomes,
CSA = 2π (3r) H
CSA = 6πr. H
Now, compare the CSA of the cylinder to find the height
6πrH = 2πrh
H = 2πrh / 6πr
H = (1/3)h
Hence, the new height of the cylinder is one-third of the original height.