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?

(a) $\frac{x^2}{2\mathrm{\pi }}$

(b) $\frac{x}{2\sqrt{\mathrm{\pi }}}$

(c) $\frac{\sqrt{2x}}{\mathrm{\pi }}$

(d) $\frac{\mathrm{\pi }}{2\sqrt{x}}$

Answer 1

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

……. (1)

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

It is given that V₁ =1/4 V₂Therefpre,

Hence, the correct option is (b)