Volume of Hyperboloid of One Sheet

Calculus Level 5

\[ \large \dfrac{x^2}{64}+\dfrac{y^2}{81}-\dfrac{z^2}{100}=1 \]

If the volume \(V\) of the hyperboloid (bound by \(0\leq z\leq 1\)) of one sheet described above can be expressed as \(V=\dfrac{A\pi }{B}\), where \(A\) and \(B\) are coprime positive integers, find \(A+B\).

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