Q. 233.8( 50 Votes )
Prove that the vo
Let r and h be the radius and height of the cone respectively inscribed in a sphere of radius R.
Let V be the volume of cone.
And height of cone h = R +
After solving this we get,
So, when, , then < 0
Then, by second derivative test, the volume of the cone is the maximum when
So, when, , h = R +
Therefore, V =
Therefore, the volume of the largest cone that can be inscribed in the sphere is the volume of the sphere.
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