17) Imagining extending all the faces of a cube, into how many regions is the entire space (including the interior of the cube) divided?
(A) 9 (B) 16
(C) 24
(D) 27
(E) 32.
17) The answer is (D). The number of regions is indeed $1+6+12+8=27$. 1 is the cube itself, 6 are the regions that "border" one of the 6 faces of the cube, 12 border each of the 12 edges, and 8 border the vertices.