Q. 25 4.7( 3 Votes )

Show that the height of the cone of maximum volume that can be inscribed in a sphere of radius 12 cm is 16 cm.

Answer :

Let h and r be height and radius of the required cone.

R be the radius of the sphere.

Now, it must be understood that for the cone to have maximum volume, the axis of cone and sphere must be the same.

Let OD = x


AD = AO + OD = 12 + x

The roots of this quadratic equation is - 12 and 4. As - 12 is not possible, we have x = 4.

Therefore, the volume is maximum when the x = 4.

Therefore the height of the cone = R + x = 12 + 4 = 16cm.

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