2008 AMC 8 Problem 16

Attempt Problem 16 of the 2008 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2008 AMC 8 solutions, or check the answer key.

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16.

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?

1:6 \:1 : 6

7:36 \: 7 : 36

1:5 \: 1 : 5

7:30 \: 7 : 30

6:25 \: 6 : 25

Answer: D
Concepts:surface areavolumecube geometry
Difficulty rating: 1150
Solution:

The shape uses 77 unit cubes, so its volume is 77 cubic units.

The center cube has no exposed faces. Each of the six outer cubes has 55 exposed faces, for a total surface area of 65=306\cdot5=30 square units.

The ratio of volume to surface area is 7:307:30.

Thus, D is the correct answer.

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