The Bulging Box

Calculus Level 5

The volume of the region of space satisfying all of the following inequalities:

\[\begin{align} x^2+y^2 &\le 1 \\ x^2+z^2 &\le 1 \\ y^2+z^2 &\le 1 \end{align} \]

can be written as \(a+b\sqrt{c}\), where a, b, and c are integers, and c is positive and square-free. Find \(a+b+c\).

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