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Question

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


A

tripled

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B

constant

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C

one sixth

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D

one third

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Solution

The correct option is D

one third


Explanation for the correct option.

Let the height of the cylinder is hand radius is r.

We know that curved surface area of the cylinder is given by:

A=2πrh

Let changed height is h'.

Given: The radius of a cylinder is tripled but its curved surface area is unchanged.

Therefore,

2π3rh'=2πrhh'=13h

Hence, the changed height is one-third of the previous height.

Option D is the correct answer.


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