If the radius of a cylinder is doubled, the height of the cylinder should be halved in order to keep the curved surface area unchanged.
True
False
A
False
B
True
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Solution
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Let, the original radius be r cm and original height be h cm
Formula for Curved Surface Area of the cylinder=2πrh
For new cylinder,
New Radius r1=2r cm
Let, New height be h1 cm
Now, according to question
2πrh=2πr1h1
⇒rh=2rh1
⇒h1=h2
This proves that height must be halved to have the same curved surface area when radius is doubled.
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