Question

Find the volume (in ${\text{cm}}^3$) of the largest right circular cone that can be cut off from a cube of edge $4.2\text{cm}$.

Answer 1

As can be observed from the figure of largest cone in a cube, the radius, $r=\frac{a}{2}$

and Height, $h=a$

$\text{Volume of cone}=\frac{\pi r^{2}h}{3}=\frac{\pi {\left(\frac{a}{2}\right)}^{2}a}{3}=\frac{\pi a^3}{12}$

$=\frac{\pi }{12}(4.2{)}^3{\text{cm}}^3=19.38{\text{cm}}^3$.