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Math Help - Inscribed Square

  1. #1
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    Inscribed Square

    A square is inscribed in a small circle of a sphere whose great circle has a radius of 9cm. If the plane of the square is 6cm from the center of the sphere, find the perimeter of the square.

    Help please! thanks!
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  2. #2
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    Hello, reiward!

    Did you make a sketch?


    A square is inscribed in a small circle of a sphere with radius 9 cm.
    If the plane of the square is 6cm from the center of the sphere,
    find the perimeter of the square.
    Code:
                  * * *
              *     |   x  *
          A o - - - + - - - o B
           *        |     *  *
                   6|   *
          *         | *  9    *
          *         o         *
          *         C         *
    
           *                 *
            *               *
              *           *
                  * * *

    AB is the side of the square.

    Pythagorus says: . x^2 + 6^2 \:=\:9^2 \quad\Rightarrow\quad x^2 \:=\:45 \quad\Rightarrow\quad x \:=\:3\sqrt{5}

    . . Then: . AB \;=\;2x \;=\;6\sqrt{5}


    The perimeter is: . 4\left(6\sqrt{5}\right) \;=\;24\sqrt{5}\text{ cm}

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