Question

A closed cylinder of given volume will have least surface area when the ratio of its height and base radius is

• A. 2 : 1
• B. 1 : 2
• C. 2 : 3
• D. 3 : 2

Answer 1

The correct option is A 2 : 1

$v=\pi r^{2}h$
$surface=2\pi r^2+2\pi rh$
$=2\pi (r^2+\frac{v}{\pi r})$
$\frac{d\left(surface\right)}{dr}=(2r-\frac{v}{\pi r^2})2\pi$
$r^3=\frac{v}{2\pi }$
$r=(\frac{v}{2\pi }{)}^{\frac{1}{3}}$
$h=\left(2{)}^{\frac{2}{3}}\right(\frac{v}{\pi }{)}^{\frac{1}{3}}$
$h:r=2:1$