Question

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

Options

• tripled

• constant 

• one sixth

• one third

Answer 1

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

Explanation:

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  ...[Given]

⇒ 6πr × h’ = 2πrh

⇒ `h^’ = (2pirh)/(6pir)`

∴ `h^’ = 1/3 h`

Hence, the new height will be `1/3` of the original height.