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Question

Question 4
If the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved.

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Solution

True.
Let the radius of a cylinder be r and height be h.

Curved surface area of a cylinder =2πrh

Let the new radius, r1=2r and height be H.

Curved surface of the cylinder is not changed; therefore,

2πrh=2π(2r)×H

2πrh=4πrH

H=2πrh4πrH=h2

Hence, the height must be halved.

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