Find the dimensions (height and radius) of the cone that has the maximum volume?Given that a right circular cone is inscribed in a sphere of radius 15cm.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

You need to find the dimension of height of cone such that:

`h = 15 + sqrt(15^2 - r^2)`  (r expresses the radius of cone)

You need to remember the formula that expresses the volume of cone such that:

`V = (pi*r^2*h)/3`

You need to substitute 15 + sqrt(15^2 - r^2) for h in formula of volume such that:

`V = (pi*r^2*(15 + sqrt(15^2 - r^2)))/3`

`V(r) = 5pi*r^2 + pi*r^2*sqrt(15^2 - r^2)/3`

The problem provides the information that the cone has maximum volume, hence you need to differentiate the volume with respect to r, such that:

`V'(r)...

(The entire section contains 271 words.)

Unlock This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial
Approved by eNotes Editorial Team