A cube is cut by a sharp knife along the plane

MATHEMATICS · Single correct · ISC · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

A cube

C = \{(x, y, z) | 0 \le x, y, z \le 1\}

is cut by a sharp knife along the plane

x = y, y = z, z = x

. If no piece is moved until all three cuts are made, the number of pieces is (1) 6 (2) 7 (3) 8 (4) 27