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Hello. I'm having problems with a couple of Calculus questions that involve maximums of geometric shapes.

The first one is:

1. Find the dimensions and minimum volume of a right circular cone which can be circumscribed about a sphere of diameter 8.

What I have is used similar triangles.
The two ratios are y/4 = (y+4)/(x+4).

I ended up isolating for x and got x = [(4y+16)/4] - 4.

Then I used this information to plug into the volume of a cone formula but I can't get it right so can someone tell me what I'd do next or tell me if I made a mistake? Any help is appreciated. Thanks.

2. A right square0based prism has to fit inside a cone that has a height of 9.0cm and a radius 4.0cm, so that the top four corners of the prism touch the cone. What are the dimensions of the prism of the maximum volume? What is the maximum volume?

Again, I used similar triangles for this questions.

My ratios are 9/4 = h/(4-x). Then I isolated h and got h = 9 - 2.25x.
At this point, I plugged in h into the formula for the volume of a prism, this one being x^2h but I compared my answer with another persons and when they isolated h, they had h = 1.125 because their ratio was 9/4 = h/(1/2)x.

So I'm unsure what is correct.

Any help is much appreciated. Thanks a lot.

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