1090.91 – The Pierced Cube

Tags:Problem Set 13Pre-Calculus MathPre-Calculus

Two of the holes in the cube go all the way through. The third only goes halfway. How many faces does the whole thing have?

  1. 22
  2. 23
  3. 24
  4. 25
  5. 26


First, there are 6 faces of the original cube.

We may assume that it is the hole from the top that only goes halfway through. Then the floor of the space inside the cube at the end of the hole from the top is a single new face that looks like the figure below.

Four short tunnels lead into this central space. Each has two side walls and a ceiling. That's 3 per side hole for another 12 faces.

Finally, the 'chimney' has four side faces.

Adding we get 6 + 1 + 12 + 4 = 23 faces. The answer is b.