Problem:
A shape is created by joining seven unit cubes, as shown. What is the ratio of the volume in cubic units to the surface area in square units?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The volume is cubic units. Six of the cubes have square faces exposed. The middle cube has no face exposed. So the total surface area of the figure is square units. The ratio of the volume to the surface area is .
The volume is cubic units. There are five unit squares facing each of six directions: front, back, top, bottom, left and right, for a total of square units of surface area. The ratio of the volume to the surface area is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions