MathNet 2007-part-01 — 187 problems (EN–VI) Question 135

Given a unit cube $ABCD-A_1B_1C_1D_1$, construct a ball with point $A$ as the center and of radius $\frac{2\sqrt{3}}{3}$. Then the length of the curves resulting from the intersection between the surfaces of the ball and cube is ______.