Q. 20 5.0( 5 Votes )

Show that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to 2/3 of the diameter of the sphere.

Answer :

Let the radius and height of cone be r and h respectively

Radius of sphere = R

R2 = r2 + (h - R)2

R2 = r2 + h2 + R2 - 2hR

r2 = 2hR - h2 …1

Assuming volume of cone be V

Volume of cone, (from equation 1)

Condition for maxima and minima is

4hR - 3 h2= 0

For , < 0

V will be maximum for

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.