MCQ

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

- \[\frac{x^2}{2\pi}\]
- \[\frac{x}{2\sqrt{\pi}}\]
- \[\frac{\sqrt{2x}}{\pi}\]
\[\frac{\pi}{2\sqrt{x}}\]

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#### Solution

Let V_{1} be the volume of the cylinder with radius r and height h, then

`V_1 = pir^2h` ……. (1)

Now, let V_{2} be the volume of the box, then

`V_2 = x^2 h`

It is given that V_{1} =1/4 V_{2}Therefpre,

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

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

Concept: Surface Area of Cylinder

Is there an error in this question or solution?

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