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Question
If the height of a cylinder becomes `1/4` of the original height and the radius is doubled, then which of the following will be true?
Options
Volume of the cylinder will be doubled.
Volume of the cylinder will remain unchanged.
Volume of the cylinder will be halved.
Volume of the cylinder will be `1/4` of the original volume.
Solution
Volume of the cylinder will remain unchanged.
Explanation:
We know that, the volume of a cylinder having base radius r and height h is V = πr2h
Now, If new height is `1/2`th of the original height and the radius is doubled, i.e. h' = `1/4`h and r' = 2r, then
New volume, V' = `pi(2r)^2 xx 1/4 h = 4pir^2 xx 1/4h`
= `pi^2h` = V
Hence, the new volume of cylinder is same as the original volume.
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