# 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.

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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