Question

Find the volume of the largest right circular cone that can be cut of a cube whose edge is $9cm$.

Answer 1

The base of the largest right circular cone will be the circle inscribed in the face of the cube and its height will be equal to an edge of the cube.

Radius of the base of the cone $r=\frac{9}{2}m$

Height of cone $=h=9cm$

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

volume of the cone $=\frac{1}{3}\times \frac{22}{7}\times \frac{9}{2}\times \frac{9}{2}\times 9{cm}^3=\frac{2673}{14}{cm}^3=190.93{cm}^3$