Wedding cake

Calculus Level pending

So recently I was at my aunt's wedding, and low and behold, I couldn't help my self but think of how I could make a problem out of this. So here it is (this and several other problems I'm about to post are based off of this problem)


A wedding cake of 14 levels is modeled by rotating the function \(y=\lfloor x \rfloor +1\) from \(0\leq x < 14\) around the x-axis. If the answer can be represented as \(a\pi\), find a.

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