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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