Sphere inside a cone problem.

I'm taking a test soon, the next problem is one of which I'll be facing on it, and I would like to ask you guys to help me know how to solve it, as well as which is what I need to study in order to solve alike problems.

Suppose that a sphere of radius 1 is inscribed in a right circular cone with radius *r* and height *h*.

(1) Express *r* in terms of *h*.

http://img74.imageshack.us/img74/9938/circleos6.jpg

(2) Find the minimum of the volume of such a right circular cone.

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Now the answer for (1) is supposed to be

http://img513.imageshack.us/img513/5246/circle2jf4.jpg

Why is this so?

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And for (2)

Thanks.