The following e-mail was sent to me:
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I am an engineering geologist. I am involved in a case where
a landowner filled in a stream with a road, several bridges, and
an island. The local regulatory agency would like to estimate
the volume of fill placed in the stream. That's my job. I have
been able to calculate most of the volume by slicing the fill
into cross sections and calculating the area of cross section
and then multiplying the area for whatever length I decide to
evaluate. My problem is where some cross sections are attached
at a pivot
point and I have a angular "length" to evaluate. For
example how would you calculate the volume where two trapezoid
cross sections of different areasthat have a common pivot point
and are separated by 50 degrees ? Or moreeasily, what is the volume
of a trapezoid that sweeps across an angle of 50 degrees?
No wonder I am a Geologist, couldn't handle the math ! Thanks
for your
help.
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Interpret what he is asking for and devise an easily understood strategy for estimating the volume he is looking for.
There is a pivot point P and a distance R from the pivot point to the center of the trench. We have a trapezoid cross section with bases a and b and height h. The pivot angle is 50 degrees.
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Devise a spread sheet that can be used to estimate the volume given input of the dimensions of the trapezoid, the distance from the pivot point to the center of the trench, and the pivot angle.