The problem is to find the radius and height of the open right circular cylinder of largest surface area that can be inscribed in a sphere of radius a. What is the largest surface area?(adsbygoogle = window.adsbygoogle || []).push({});

The open cylinder's surface area will be

[tex] f(h,r) = 2 \pi r h [/tex]

I am not really sure about the sphere, because I'm not really sure about the constraints that would apply. It looks like it would just be

[tex] a^2 = r^2 + h^2 + r^2 = 2r^2 +h^2[/tex], but this would only be if the cylinder is centered about the origin. But I guess that since it is a sphere, and perfectly symmetrical, then trying to squeeze the cylinder in diagonally would be the same as along the origin. Right?

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# Homework Help: Cylinder inscribed in sphere

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