# A challenging volume problem

1. Dec 9, 2011

### JCienfuegos

Hello everyone
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

2. Dec 9, 2011

### 256bits

Since the volune of a sphere is
V = (4 pi ) )r^44 / 3

Then the answer is somewhere between r and 2r.
( a range is an answer ) :)

3. Dec 10, 2011

### JCienfuegos

I tried using this trick in high school. The teacher said what is sin342 or something like that and I put "something between -1 and 1". I got that question wrong.

4. Dec 12, 2011

### 256bits

I now get the leash to be 1/10 longer than the radius of the sphere.
Is that correct?

5. Dec 13, 2011

### JCienfuegos

Well, that is not the answer i got. Now that think about it, my solution may be wrong, but I cannot think why.