This time a Paraboloid!

Calculus Level pending

There's a Paraboloidal Tank having depth $$H$$ and Diameter of top Circular Opening as$$D$$ .If the Surface Area of the tank can be expressed as: $$\large\frac { a\pi D }{ b\sqrt { H } } \left[ { \left( H+\frac { { D }^{ e } }{ fH } \right) }^{ \frac { c }{ d } }-{ \left( \frac { { D }^{ e } }{ fH } \right) }^{ \frac { c }{ d } } \right]$$ where $$a,b,c,d,e,f$$ are positive integers the submit:$$a+b+c+d+e+f$$ as answer.

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