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Geometry Level 4

Let \(ABCD\) be a trapezium with \(AB\) and \(CD\) parallel. We have \(AB=3, BC=AD=3\sqrt { 2 }, CD=9\). Calculate the sum the volumes of the solids obtained by spinning the trapezium around all its sides.

If the total volume can be written as \((a+b\sqrt { c } )\pi \). Calculate \(a-9b+c\).

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