A sector with central angle is cut from a circle of radius 12 inches, and the edges of the sector are brought together to form a cone. Find the magnitude of so that the volume of the cone is a maximum.

See attached figure

thanks

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- May 10th 2008, 07:30 PM #1

- May 10th 2008, 09:50 PM #2
There's stuff in this link that should solve-enable you: Math Forum - Ask Dr. Math

- May 11th 2008, 09:39 AM #3

- May 11th 2008, 10:48 AM #4
You are dealing with two different radi:

- The radius of the sector which is the slanted line from the tip of the cone to it's edge

- the radius R of the base circle of the cone.

You know the length l of the arc of the sector:

which has the same length as the circumference of the base circle:

The slanted line s, the radius of the base cicle R and the height of the cone form a right triangle. Use Pythagorean theorem:

Plug in the terms of R and h into the equation of the volume. You'll get a function with respect of :

To calculate the maximum volume you have to derive this function and solve for the equation:

EDIT: Removed my typo in the last equation.