The volume of a cylinder of radius `r` is `1/4` of the volume of a rectangular box with a square base of side length `xdot` If the cylinder and the box have equal heights, what is `r` in terms of `x ?` (a) `(x^2)/(2pi)` (b) `x/(2sqrt(pi))` (c) `(sqrt(2x))/pi` (d) `pi/(2sqrt(x))`

Explanation

given that,

volume of cylinder `=(1/4)volume of rectangular box`

`pir^2h=(1/4)(x^2)h`

[ since height of both are same and x^2 is area of base of rectangular base]

so,`r = x/{2xxpi^(1/2)}`

so answer is b)