Question

If the radius of a cylinder is doubled keeping its lateral surface area the same
then what is its height?​

Answer 1

The lateral surface area of a cylinder is A=

$2\pi \: rh$

If r is doubled let H be the height, then new curved surface area is

$2\pi \: 2rH = 4\pi \: rH$

Now, since the lateral surface area is kept same

$2\pi \: rh = 4\pi \: rH \\ = > H = \frac{h}{2}$

Hence the new height is half the original height.

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