If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the original cylinder? (a) 4 (b) `1/(sqrt(2))` (c) 2 (d) `1/2`

Explanation

let radius `=r`

and height `=h`

so volume `v=pixx(r^2)h`

let in new case radius `R=xr`
and
height `H=2h`
so new volume `V=pixx(xr)^2(2h)`

since in both case,

volume are equal so,

`pixx(r^2)h=pixx(xr)^2(2h)`

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