Question

The height of the cylinder of maximum volume that can be inscribed in a sphere of radius $R$ is

• A. $\frac{2R}{3}$
• B. $\frac{R}{3}$
• C. $\frac{2R}{\sqrt{3}}$
• D. $\frac{R}{\sqrt{3}}$

Answer 1

The correct option is C $\frac{2R}{\sqrt{3}}$

$\frac{h^2}{4}+r^2=R^2$
Volume of cylinder $=\pi r^{2}h$
$=\pi (R^2-\frac{h^2}{4})h$
$\frac{dv}{dh}=\pi (R^2-\frac{3h^2}{4})$
$0=R^2-\frac{3h^2}{4}$
$h=\frac{2R}{\sqrt{3}}$