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

Height (cylinder) $=$ Side(cube)

$h=x\text{cm}$

Radius (cylinder) $=\frac{\text{side}}{2}$

$r=\frac{x}{2}\text{cm}$

Volume of cylinder that can be cut $=\pi r^{2}h$

$=\pi \frac{x^2}{4}.x$

$=\frac{\pi x^3}{4}{\text{cm}}^3$