Question

A hemisphere of radius 5 sits on a horizontal plane. A cylinder stands with its axis vertical, the center of its base at the center of the sphere, and its top circular rim touching the hemisphere. Find the radius and height of the cylinder of maximum volume.

Answer 1

If the top circular rim of the cylinder touches the top of the hemisphere, that would give you the height of the cylinder. Also if the center of its base and center of the sphere rests at the same point, that means they have the same sized base. Using these information, you can find the answer

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Answer 2

Is there just an easy way to find the radius and the height with not much work? Also thank you for your help!

Answer 3

Maybe a dumb down version

Answer 4

that square thing outside is the cylinder and that circular thing i s the ehmesphere, as you can see they have same height and radius