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This problem is similar to a problem that appeared sometime back on this website called "last geometry challenge, very difficult!"

The problem was this: There is a circular field of grass of radius r surrounded by a fence. If aa sheep is tethered to the fence, how long should its leash be so that it eats only 1/2 of the grass in the circle.

I propose making this into a 3D problem. Make the circle of grass a sphere of jelly surrounded by a spherical metal cage. How long should the leash be if an animal is tethered to the surrounding spherical metal cage so that it eats only 1/2 of the volume of jelly.

Ill post the answer in a couple of days if anyone is interested.

Julian

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# A challenging volume problem

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