From a wooden cube of side  $\text{'}\mathrm{x}\text{'}$ cm, if a right circular cylinder of maximum volume is cut, then the volume of this cylinder is

Side (cube)  = xcm
Height (cylinder)  Side(cube)
$\mathrm{h}=\mathrm{x}\text{cm}$
Radius (cylinder)  $=\frac{\text{side}}{2}$
$\mathrm{r}=\frac{\mathrm{x}}{2}\text{cm}$
Volume of cylinder that can be cut $={\mathrm{\pi r}}^2\mathrm{h}$
$=\mathrm{\pi }\frac{{\mathrm{x}}^2}{4}.\mathrm{x}$
$=\frac{{\mathrm{\pi x}}^3}{4}{\text{cm}}^3$