Question

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

Answer 1

Since the edge of cube is 9 cm this will be the altitude of the cone. 
The radius of circular cone will be 9:2=4.5 cm. 
The volume of cone is given by formula: , where R is the radius and H the altitude of cone. Since we are asked for the largest cone, its volume must be equal or less than the volume of cube. We write: 

 so answer will be 60 .75 [pie]cm³

Answer 2

diameter of cone = height of the cone = side of cube = 9cm
volume of cone = 1/3 × 22/7 × r × r × h
radius of cone = 9 / 2 cm
= 1/3 × 22/7 × 9/2 × 9/2 × 9
= 2673/14
=190. 9 cm cube