Hey...I need ur Help!!! Abt calculus!!!!?

Question

Find the dimensions of a right circular cone of minimum volume which can be circumscribed about a sphere of radius 12cm...

Answer 1

So what's the problem?

Answer 2

If I had more time I would work out the details. All I can do is outline how to do the problem.

1. It reduces to a 2-dimensional problem: Find the dimensions of a isoceles triangle of minimum area which can be circumscribed on a circle of radius 12 cm. When you get the answer to this, all you have to do is rotate the triangle into 3-dimensions around it's center-height axis.

2. Find a function that describes the area of the triangle as a function of the center height -- which involves trig functions of the angle, as the angle varies from 0 to 90 degrees.

3. differentiate this function.

4. set the function = 0 (to find the minima, maxima) and solve for f'(theta)

4a. determine if it is a minima (the only solution probably is)

5. plug this theta angle back into the original equation to obtain the area

6. convert the area back into a cone volume.

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Answer 3

A right circular cone of 'minimum' volume? Do you mean what is the maximum possible cone volume that could fit in this sphere?
Because, the minimum volume would be a very tall cone (approaching the diameter of the sphere) with a base that approaches zero. But this doesn't seem like a calculus problem but a logic problem.