word problem

C

calculusclueless

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Apr 19, 2011
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i can't figure out this problem to save my life.

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

any help would be great thank you
 
You WILL have to start showing SOME work. You can't have NO idea. What a suggestion!
 
i know that the formula for the volume of a cone is v=1/3(pi)(r^2)h.

i really don't know where to go from there.
 
What do you know of the "slant height"? It used to be the radius of the circle. Some Theorem of Pythagorus will help you find the radius of the cone. You must also know something of the "Lateral Surface Area". What's the formula for that on a Right Circular Cone?

Ask questions of yourself. You now much more of cones than the formula for the volume.
 
in order to use pathagorean theorem tho i need the base or the height too. all i know is that the hypotenus is 12^2... i don't know what the radius or height of the cone is.
 
That's why I mentioned the :Lateral Surface Area. You DO know that. It comes immediately from the construction.
 
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