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# Hard Geo Problem

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Consider two nonparallel planes $X,Y$ that go through to the center of a sphere of radius one. This cuts the sphere into 4 parts $A,B,C,D$. The two parts $A,B$ are on the same side of $X$, such that the volume of $A$ is greater than the volume of $B$. If the expected value of the volume of $A$ can be expressed as $\frac{a}b\cdot\pi$, where $\gcd(a,b)=1$ find $a+b$.

Feb 2, 2021

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The expected vaue is 5/12*pi, so a + b = 5 + 12 = 17.

Feb 3, 2021
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Can you explain how you got that?

XxGuestxX  Feb 3, 2021
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As follows (I think!):

Feb 3, 2021
edited by Alan  Feb 3, 2021
edited by Alan  Feb 3, 2021