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Math Help - Solid Geometry Problem (Frustum)

  1. #1
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    Solid Geometry Problem (Frustum)

    Find the total area of the frustum of a regular square pyramid which is inscribed in the frustum of a cone whose upper and lower base diameters are 4ft. and 6ft.,respectively, and whose altitude is 12ft.

    The answer is 196sq ft.

    I don't know where to start can someone help me with solutions?
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Solid Geometry Problem (Frustum)

    The four slant edges of the truncated pyramid will be touching the cone within which it is inscribed. Thus, the diameter of the cone at some height is equal to the diagonal of the square pyramid. If you know the diagonal of a square, then what are the side lengths?

    Once you have the side lengths of the top and bottom of the truncated pyramid, you know the area of the top and bottom, the square portions. What shape are the sides of the truncated pyramid? How can you find their areas?
    Thanks from PhillipMasagca
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