# Volume of solids of revolution

Calculus Level pending

Let $${\bf a }$$ and $${\bf b }$$ be real positive constants.

The volume of the region bounded by the curve $${\bf x = \frac{a}{b} * \sqrt{b^2 - y^2}, y = 0 \: and \: y = b }$$, when revolved about the line $${\bf x = a }$$, can be expressed as $${\bf a^2b\pi * (\frac{m}{n} - \frac{\pi}{p}) , }$$ where $${\bf m, }$$ $${\bf n }$$ and $${\bf p }$$ are coprime positive integers.

Find $${\bf m + n + p }.$$

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