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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? - Mathematics


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?


  • \[\frac{x^2}{2\pi}\]


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


  • \[\frac{\pi}{2\sqrt{x}}\]

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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))`


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RD Sharma Mathematics for Class 9
Chapter 19 Surface Areas and Volume of a Circular Cylinder
Q 15 | Page 29
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