Q. 124.5( 6 Votes )

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

Answer :

Volume of cone = πr^{2}h

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 = × × 7^{2} × 14

= × 22 × 49 × 2

=

=

= 718.67 cm^{2}

Therefore, volume of the largest right circular cone that can be cut out of the cube is 718.67 cm^{2}

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