Three Cylinders, Continued

What is the volume of the intersection in the last blog posting? To compute that we decompose the intersection into 7 parts, three caps, and one cube, using PovRay again. That took me another hour.

Three cylinders in seven parts

The top cap can be integrated along its center, and the cube has side length

\(1/\sqrt{2} \)

If I did not a mistake the volume is

\(\dfrac{4}{\sqrt{2}} + 24(\dfrac{2}{3}-\dfrac{5}{6\sqrt{2}}) \)

This is a bit more than 4.

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