MathDB

Math Prize 2022 Problem 3

Source:

October 12, 2022

Problem Statement

Let

ABCD

be a square face of a cube with edge length

2

. A plane

P

that contains

A

and the midpoint of

\overline{BC}

splits the cube into two pieces of the same volume. What is the square of the area of the intersection of

P

and the cube?