Question

The height $h$ of a cylinder is equal to the edge of a cube. If the cylinder and the cube have the same volume, what is the radius of the cylinder?

• A. $\frac{h}{\sqrt{\pi }}$
• B. $h\sqrt{\pi }$
• C. $\frac{\sqrt{\pi }}{h}$
• D. $\frac{h^2}{\pi }$

Answer 1

Answer: (A)

$\frac{h}{\sqrt{\pi }}$

Let height of the cylinder be $h$ and edge of cube be $l$

$h$ = $l$ [Given]....(i)

Volume of cylinder = Volume of cube [Given]

$\Rightarrow \pi r^{2}h=sid{e}^3$

$\Rightarrow \pi r^{2}h=l^3$

$\Rightarrow \pi r^{2}h=h^3$ ...... [From (i)]

$\therefore$ $r^2=\frac{h^2}{\pi }$

$\therefore$ $r=\frac{h}{\sqrt{\pi }}$