MathDB
1987 AMC 12 #27 - Cuts in 3D Plane

Source:

January 1, 2012
geometry3D geometryAMC

Problem Statement

A cube of cheese C={(x,y,z)0x,y,z1}C=\{(x, y, z)| 0 \le x, y, z \le 1\} is cut along the planes x=yx=y, y=zy=z and z=xz=x. How many pieces are there? (No cheese is moved until all three cuts are made.)
<spanclass=latexbold>(A)</span> 5<spanclass=latexbold>(B)</span> 6<spanclass=latexbold>(C)</span> 7<spanclass=latexbold>(D)</span> 8<spanclass=latexbold>(E)</span> 9 <span class='latex-bold'>(A)</span>\ 5 \qquad<span class='latex-bold'>(B)</span>\ 6 \qquad<span class='latex-bold'>(C)</span>\ 7 \qquad<span class='latex-bold'>(D)</span>\ 8 \qquad<span class='latex-bold'>(E)</span>\ 9