Question

An edge of a cube measures r cm. If the largest possible right circular cone is cut out of this cube, then find the volume of the cone (in $m^3$).

Answer 1

Diameter of cone = r (largest cone)

radius = $\frac{r}{2}$

height = r

volume of cone = $\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\pi [\frac{r}{2}{]}^{2}r$

$=\frac{1}{3}\pi \frac{r^2}{4}r$

$\Rightarrow \frac{1}{12}\pi r^3$