Question

The largest possible right circular cone is cut out of a cube of edge r cm. The volume of the cone is $\frac{1}{12}\pi r^3$.

Answer 1

True.

Radius of the cone = $\frac{r}{2}$
Height of the cone = r
∴ Volume of the cone =$\frac{1}{3}\mathrm{\pi }\times {\left(\frac{r}{2}\right)}^2\times r=\frac{1}{12}\mathrm{\pi }{r}^3$