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Math Help - Solid Geometry Problem

  1. #1
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    Solid Geometry Problem

    An irregular pile of earth is 15ft. high and covers 500sq ft. Its Mid-sections and level top are estimated to contain 400 and 200 sq. ft., respectively. Find the cost of removing it at 60 cents per load. If the tower measures 3 by 4 by 9 ft.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Solid Geometry Problem

    To find the volume of dirt, use the formula:

    V=\frac{h}{6}(B+4M+T)

    where h is the height of the pile, B is the area of the bottom, M is the area of the mid-section and T is the area of the top.

    Then divide this volume by the volume of the "tower" to find how many loads there are, and multiply this by 60 cents to find the total cost of removing the dirt.
    Last edited by MarkFL; August 24th 2013 at 05:14 AM.
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  3. #3
    MHF Contributor MarkFL's Avatar
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    Re: Solid Geometry Problem

    Perhaps a better formula for the volume of dirt, since the pile dies not seem to have a constant angle of repose, is:

    V=\frac{h}{6}\left(B+\sqrt{BM}+2M+\sqrt{MT}+T \right)
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  4. #4
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    Re: Solid Geometry Problem

    Granular materials form conical piles according to their angles of repose.Earth 30=40deg,sand 34 deg.Standard formula for frustum volume
    V=1/3pih(r1^2+r2^2+r1*r2)
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