If the radius of a cylinder is tripled but its curved surface area is unchanged, then its height will be
(c) one sixth
(d) one third
The correct answer is option (d) one third
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.