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3D Geometry

Source: 2005 National High School Mathematics League, Exam One, Problem 4

March 19, 2020
geometry3D geometryperimeter

Problem Statement

In cube ABCD−A1B1C1D1ABCD-A_1B_1C_1D_1, draw a plane α\alpha perpendicular to line AC′AC', and α\alpha has intersections with any surface of the cube. The area of the cross section is SS, the perimeter of the cross section is ll, then (A)\text{(A)} The value of SS is fixed, but the value of ll is not fixed. (B)\text{(B)} The value of SS is not fixed, but the value of ll is fixed. (C)\text{(C)} The value of SS is fixed, the value of ll is fixed as well. (D)\text{(D)} The value of SS is not fixed, the value of ll is not fixed either.
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