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Math Help - Radius of a sphere

  1. #1
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    Radius of a sphere

    Determine the equation of each sphere, given that the center has the coordinates (3,-2,5)

    The sphere touches the xy-plane at one point.

    This is what it says in my solution book, which I don't get.

    The radius of the sphere is the length of the perpendicular line dropped from the center of the xy-plane. Therefore, the radius is 5.
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  2. #2
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    Quote Originally Posted by chengbin View Post
    Determine the equation of each sphere, given that the center has the coordinates (3,-2,5)
    The sphere touches the xy-plane at one point.
    This is what it says in my solution book, which I don't get.
    The radius of the sphere is the length of the perpendicular line dropped from the center of the xy-plane. Therefore, the radius is 5.
    Your text is correct.
    Place a ball on your level writing table. How far its center from the table top?
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  3. #3
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    I'm not sure if I get it.

    Can someone explain it in more detail (a picture would be nice), or guide me to a place explaining this? I really suck in geometry.
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  4. #4
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    Quote Originally Posted by chengbin View Post
    I'm not sure if I get it.

    Can someone explain it in more detail (a picture would be nice), or guide me to a place explaining this? I really suck in geometry.
    the sphere's center is at the position (3,-2,5)

    note that the center's z-coordinate is 5 ... that means the center is 5 units above the xy plane.
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  5. #5
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    You said that the sphere touches the xy plane. Any point on the xy plane would have a z-coordinate of 0. If the sphere touches the xy-plane then it must do so at (3, -2, 0). The distance from the center to this point is 5, so that's why the radius is 5.


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