The Bulging Box

Calculus Level 5

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

x2+y21x2+z21y2+z21\begin{aligned} x^2+y^2 &\le 1 \\ x^2+z^2 &\le 1 \\ y^2+z^2 &\le 1 \end{aligned}

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

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