If the radius of the cylinder is tripled but its curved surface area is unchanged, then its height will be

Question

Philoid · Accepted Answer

Let H be the new height.

Curved surface area of a cylinder with radius r and height h = 2πrh

Now, according to the question, radius is tripled

Then,

Curved surface area = 2π × 3r × h = 2πrh

6πrh = 2πrh

H =

H = h

Hence ,the new height will be of the original height.