.Solution
Suppose that the cylinders are along the x- and y-axes. Then their equations are x2 + z2 < 1 and y2 + z2 < 1. For each cross-section perpendicular to the z-axis, the equations become x2 < 1 - z2 and y2 < 1 - z2 < 1, so the area of each cross-section is the area of a square with side 2(1 - z2)1/2, which is 4(1 - z2). To find the volume of the full figure, we integrate with respect to z, from -1 to 1. So the solution is
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