Question 83
Given a cube with side $10$, consider a plane passing through exactly $6$ of the midpoints of its edges; call these points $A, B, C, D, E, F$ and assume that the sides of the hexagon $ABCDEF$ each lie on a face of the cube. Then consider a second plane containing the segment $AB$ and perpendicular to the face containing $AB$. What is the volume of the part of the cube lying between the two planes?
(A) $250$
(B) $\frac{1000}{3}$
(C) $375$
(D) $\frac{1625}{3}$
(E) There is no plane with the required properties
(A) $250$
(B) $\frac{1000}{3}$
(C) $375$
(D) $\frac{1625}{3}$
(E) There is no plane with the required properties