Question

A cylinder with the greatest lateral area is inscribed in a sphere of radius $R$. Find the volume of the cylinder.

Answer 1

Volume of cylinder$=\pi \times R\times {\sin }^{2}45°\times R{\cos }^{2}45°$

$=\pi \times R^2\times \frac{1}{2}\times \frac{1}{\sqrt{2}}$

$=\frac{\pi R^2}{2\sqrt{2}}$