Answer :

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.

Then, V=

And height of cone h = R +


Now, if,

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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses

If the sum of theMathematics - Board Papers

A metal box with Mathematics - Board Papers

Show that aRD Sharma - Volume 1

Find the local maMathematics - Board Papers

Prove that the seMathematics - Board Papers

Prove that the raMathematics - Board Papers

Prove that the leMathematics - Board Papers