Bogus Solution

by b-flat, Jun 17, 2006, 3:21 PM

I have written a solution to find the volume of intersection of two cylinders that have radii of 1 and are perpendicular to each other. What is wrong with it :roll:?

Look at the cube that contains the intersection. The probability of landing in each of the cylinders is $\frac{2\pi}8$. Multiply them together to get the probability of landing in both cylinders: $\left(\frac{2\pi}8\right)^2=\frac{\pi^2}{16}$. This is the area of the intersection over the area of the cube (which is 8), so shouldn't the volume of the intersection be $8\times\frac{\pi^2}{16}=\frac{\pi^2}{2}$?

I'm amused that Saturday, I thought that that was the correct solution :o :D

reason it does not work

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