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I have drilled a hole.........

AncientMariner
Well, I did not drill it, but about 50 years ago a colleague produced this question from his book:


"A cylindrical hole six inches long has been drilled straight through the centre of a solid sphere. What is the volume remaining in the sphere?"

Enjoy!

Clive
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    Simon Barker:

    There's some ambiguities and missing information in that question.
    • What's the width (diameter) of the hole?

    • Does "straight through the centre" mean right through the sphere and out the other side, or does it only mean the hole was deep enough to get beyond the middle of the sphere?


    For an accurate result, there's a tricky complication.  The hole is being drilled into a curved convex surface.  If you drill a hole that's six incles long once it's drilled, then you have drilled away slightly more than six inches of material.


    Sorry about this Simon, but there is no missing information! However the hole is all the way through.

    Clive


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  • 0
    Simon Barker:

    There's some ambiguities and missing information in that question.
    • What's the width (diameter) of the hole?

    • Does "straight through the centre" mean right through the sphere and out the other side, or does it only mean the hole was deep enough to get beyond the middle of the sphere?


    For an accurate result, there's a tricky complication.  The hole is being drilled into a curved convex surface.  If you drill a hole that's six incles long once it's drilled, then you have drilled away slightly more than six inches of material.


    Sorry about this Simon, but there is no missing information! However the hole is all the way through.

    Clive


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