# If the radius of a cylinder is tripled

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.