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Math Help - If a cube has the volume of 1000 then what is the smallest sphere that could be circu

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    If a cube has the volume of 1000 then what is the smallest sphere that could be circu

    If a cube has the volume of 1000 then what is the smallest sphere that could be circumscribed around it?
    Is it 500√2 or 500√3
    how did you do it
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    MHF Contributor ebaines's Avatar
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    Re: If a cube has the volume of 1000 then what is the smallest sphere that could be c

    Are you looking for the radius of the smallest spehere? First determine the length of each side of the cube. Then the spehere will have a radius that reaches from the center of the cube to each corner, so use Pythagorus to determine that length. By the way, neither of your answers are correct - perhaps the volume isn't 1000 but rather 1,000,000,000?
    Last edited by ebaines; June 19th 2013 at 09:14 AM.
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    Re: If a cube has the volume of 1000 then what is the smallest sphere that could be c

    Equivalently, the length of a diagonal of a cube of side s has length s\sqrt{3} and that is the diameter of the circumscribing sphere.
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