Find the dimensions of the right circular cylinder of greatest surface area that can be inscribed inside of a sphere of radius 9.

Question

anonymous · Answer

That's a good question. I have to go to bed though. Are you having trouble with setting it up?

anonymous · Answer

For a sphere$$V=\frac{4}{3}\pi r^{3}$$ 

For a cylinder
$$SA = 2 \pi rh + 2 \pi r^{2}$$

I don't know how to go about what's been the typical method from here. I need to maximize surface area and USUALLY, the 2nd equation is equal to something. Like 2W + 2L = 40, in which you would solve for one of the variables and plug that substitution into the equation to be maximized or minimized. But I do not know how to make such a substitution in this case. All I have are equations that I'm unsure of what to do with.

anonymous · Answer

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This is what I imagine when setting up this problem. Think about the extreme cases for each of your variables. The variable r cannot be greater than 9 and the variable h cannot be greater than 18. If r is it's "max" then h would have to be it's "min", and vice versa.