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Mar 16 at 19:10 comment added Display name Nice exercise, just verified it. It's $8$ times the volume in the first orthant bounded by $x^2+y^2+z^2 \le 1$ and $x^2 + (y-1/2)^2 \ge 1/4.$ In cylindrical, these become $r^2+z^2 \le 1$ and $r \ge \sin \theta,$ leading to a simple triple integral.
Jan 20, 2018 at 20:32 history edited Faheem Mitha CC BY-SA 3.0
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S Sep 10, 2015 at 9:52 history answered Ketil Tveiten CC BY-SA 3.0
S Sep 10, 2015 at 9:52 history made wiki Post Made Community Wiki by Ketil Tveiten