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Question
If the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved.
Options
True
False
Solution
This statement is True.
Explanation:
Let the radius and height of a cylinder be r and h respectively.
Curved surface area of a cylinder = 2πrh
If the radius of a cylinder = 2r and height = H.
And curved surface area of a cylinder is not changed.
∴ 2πrh = 2π(2r) × H
`\implies H = (2pirh)/(4pir)`
`\implies H = h/2`
Hence, the height of a cylinder must be halved.
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