MathDB

2

Part of 1985 National High School Mathematics League

Problems(2)

Both Analytic Geometry and 3D Geometry

Source: 1985 National High School Mathematics League, Exam One, Problem 2

2/23/2020
PQPQ is a chord of parabola y2=2px(p>0)y^2=2px(p>0) and PQPQ pass its focus FF. Line ll is its directrix. Projection of PQPQ on ll is MNMN. The area of curved surface that PQPQ rotate around ll is S1S_1, the area of spherical surface of the ball with diameter of MNMN is S2S_2, then (A)S1>S2(B)S1<S2(C)S1≥S2(D)\text{(A)}S_1>S_2\qquad\text{(B)}S_1<S_2\qquad\text{(C)}S_1\geq S_2\qquad\text{(D)} Not sure
analytic geometrygeometry3D geometryconicsparabola
3D Geometry Problem

Source: 1985 National High School Mathematics League, Exam Two, Problem 2

2/24/2020
In cube ABCD−A1B1C1D1ABCD-A_1B_1C_1D_1, EE is midpoint of BCBC, F∈AA1F\in AA_1, and A1F:FA=1:2A_1F:FA=1:2. Calculate the dihedral angle between plane B1EFB_1EF and plane A1B1C1D1A_1B_1C_1D_1.
geometry3D geometry