Question

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 x. If the cylinder and the box have equal heights, what is r in terms of x?

Options

• \[\frac{x^2}{2\pi}\]

   

• \[\frac{x}{2\sqrt{\pi}}\]
• \[\frac{\sqrt{2x}}{\pi}\]

   

• \[\frac{\pi}{2\sqrt{x}}\]

Answer 1

Let V₁ be the volume of the cylinder with radius r and height h, then

`V_1 = pir^2h` ……. (1)

Now, let V₂ be the volume of the box, then

`V_2 = x^2 h`

It is given that V₁ =1/4 V₂Therefpre,

`pi r^2 h = 1/4 x^2 h`

`⇒ r^2 = x^2/(4pi) ⇒ r = x/(2sqrt(pi))`