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Given a solid sphere of radius R, remove a cylinder whose central axis goes through the center of the sphere.

In a solid sphere I did a diametral hole with a cylindrical drill. I know that the distance between the two border holes formed is 6cm. How can I calculate the remainder volume in the sphere?

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    That's a solid of revolution, so you could use the usual integration methods.2012-11-02
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    I think you're out of luck unless you know the radius of the sphere and/or of the cylinder.2012-11-02
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    @rschwieb: No, that's a "well"-known puzzle. The volume does not depend on the radius of the sphere.2012-11-02
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    My teacher said that is not necessary use calculus, and you don't need any radius.2012-11-02
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    If you know the radius is not important, just imagine a sphere of diameter $6$cm. Then the removed cylinder has negligible volume, so the object must have volume $(4/3)27\pi = 36\pi$.2012-11-02
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    That's correct! 36 pi is the answer. But I didn't understand.2012-11-02
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    @ypercube That's interesting. Unfortunately it is not well-known enough to have crossed my radar before now :)2012-11-02
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    I Understood =D2012-11-02

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