Question

The height h of a cylinder equals the circumference of the cylinder. in terms of h, what is the volume of the cylinder ?

(a) $\frac{h^3}{4\pi }$ (b) $\frac{h^2}{2\pi }$

(c) $\frac{h^3}{2}$ (d) $\pi h^3$

Answer 1

In a cylinder,

h= circumference of the cylinder

$\therefore$ Radius (r) $=\frac{Circumference}{2\pi }=\frac{h}{2\pi }$ Now volume = $\pi r^{2}h=\pi {\left(\frac{h}{2\pi }r\right)}^2\times h$

=$\pi \times \frac{h^2}{4{\pi }^2}\times h=\frac{h^3}{4\pi }$

Hence the correct answer is (a) $\frac{h^3}{4\pi }$