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Math Help - Sphere equation

  1. #1
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    Sphere equation

    Find an equation of the largest sphere contained in the cube determined by the planes x = 2, x = 6,; y = 5, y = 9; and z = -1, z = 3.

    I'm going to guess that I need to use the distance formula. I don't know how to apply the result to this problem, however.

    Are these plains the boundaries of the sphere with the distance being the diameter?

    Thanks!
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  2. #2
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    Hello, Truthbetold!

    Find an equation of the largest sphere contained in the cube
    determined by the planes: . x = 2,\;x = 6,\;y = 5,\;y = 9,\;z = -1,\;z = 3

    Are these planes the boundaries of the sphere with the distance being the diameter?
    Yes!

    You don't need the Distance Formula . . . just some visualization.

    \text{The distance between the planes }\,x = 2\,\text{ and }\,x = 6\,\text{ is }\,4\text{ units.}
    . . And they said it was a cube, didn't they?

    Can you see that the radius of the sphere is 2 ?


    The center of the sphere must be halfway between the planes.

    \text{Halfway between the planes }\,x = 2\,\text{ and }\,x = 6\!:\; x = 4

    \text{Halfway between the planes }\,y = 5\,\text{ and }\,y = 9\!:\; y = 7

    \text{Halfway between the planes }\,z = \text{-}1\,\text{ and }\,z = 3\!:\; z = 1


    The center is (4,7,1) and the radius is 2.

    Go for it!
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