Q12 of 67 Page 193

Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 14 cm.

Volume of cone = πr2h


For volume to be largest the radius of base of cone ‘r’ and height of cone ‘h’ should be maximum


In a cube whose edge is 14 cm



As it can be seen from the figure that the maximum height of cone can be 14 cm and also the maximum diameter can be 14 cm


Radius = r = = 7 cm


Height = h = 14 cm


⇒ Volume of cone = × × 72 × 14


= × 22 × 49 × 2


=


=


= 718.67 cm2


Therefore, volume of the largest right circular cone that can be cut out of the cube is 718.67 cm2


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