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If a square prism is inscribed in a right circular cylinder of radius 3 and height 6, the volume inside the cylinder but outside the prism is:
Volume of the cylinder is pi * r^2 * h = pi * 9 * 6 = 54pi. Volume of prism = Bh, where B is the area of the square base, which is 3 * square root of 2 on a side.
Thus, Bh = (3 * sqrt(2))^2 * 6 = 108.
Therefore, the desired volume is 54pi - 108, which is approximately 61.6.