# A really weird problem

Calculus Level 4

A tunnel is defined by $$y = \sin x + 5$$ revolved around the x-axis within the domain $$x \in [0, 20 \pi ]$$. Suddenly, the whole tunnel is filled completely with cement. Magic happens and only the cement cast is left. If $$V$$, the volume of the cement cast in cubic units, can be represented in the form $$a \pi^{b}$$, where $$a$$ and $$b$$ are integers, find $$a+b$$.

NB: Please evaluate the integral by hand, or you'll miss out on the fun!

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