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Math Help - Weird Geometry Problem

  1. #1
    Newbie
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    May 2005
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    Weird Geometry Problem

    Any insight on this one?

    Given: 1. Sphere with diameter = 3 inches
    2. Lateral edge of the square pyramid inside of the sphere is 2 inches
    and the base is 2 inches

    Find: If you made 100 of these items, how many gallons of solution are
    needed to fill the voids?

    Hint: [1 ft = about 7.5 gallons]
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  2. #2
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    May 2005
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    does anyone know how to do this one?
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  3. #3
    Junior Member
    Joined
    Apr 2005
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    35
    Use
    V = 4/3 * Pi * r^3 for sphere
    V = 1/3 * a^2 * h for pyramid where a is the length of the base.
    You get,
    Volume of Sphere = 4/3 * Pi * (3/2)^3
    Volume of Pyramid = 1/3 * 4 * h

    Now you need h, use the formula (1) here http://mathworld.wolfram.com/SquarePyramid.html

    You should get h = root(2), so
    Volume of Pyramid = 4/3 * root(2)

    Now,
    Volume of void = Volume of sphere - Volume of pyramid
    Total number of gallons required is 100 * Volume of void.
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