Question

From a given metal sheet a cylindrical vessel without lid having maximum capacity is made then the ratio of the height and the base radius is

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

Answer 1

The correct option is D 1 : 1

$A=$ surface area $=\pi r^2+2\pi rh$
volume$=\pi r^{2}h$
$v=\frac{r}{2}(A-\pi r^2)$
$\frac{dv}{dr}=\frac{1}{2}(A-\pi r^2-2\pi r^2)$
$r=\sqrt{\frac{A}{3\pi }}$
$h=\sqrt{\frac{A}{3\pi }}$
$r:h=1:1$