Difference between revisions of "2008 AMC 8 Problems/Problem 16"
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| − | ==Problem | + | ==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? | 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? | ||
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<math>\textbf{(A)} \:1 : 6 \qquad\textbf{ (B)}\: 7 : 36 \qquad\textbf{(C)}\: 1 : 5 \qquad\textbf{(D)}\: 7 : 30\qquad\textbf{ (E)}\: 6 : 25</math> | <math>\textbf{(A)} \:1 : 6 \qquad\textbf{ (B)}\: 7 : 36 \qquad\textbf{(C)}\: 1 : 5 \qquad\textbf{(D)}\: 7 : 30\qquad\textbf{ (E)}\: 6 : 25</math> | ||
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| + | ==Solution== | ||
| + | The volume is of seven unit cubes which is <math>7</math>. The surface area is the same for each of the protruding cubes which is <math>5\cdot 6=30</math>. The ratio of the volume to the surface area is <math>\boxed{\textbf{(D)}\: 7 : 30}</math>. | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2008|num-b=15|num-a=17}} | {{AMC8 box|year=2008|num-b=15|num-a=17}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 18:25, 8 August 2021
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?
![[asy] import three; defaultpen(linewidth(0.8)); real r=0.5; currentprojection=orthographic(1,1/2,1/4); draw(unitcube, white, thick(), nolight); draw(shift(1,0,0)*unitcube, white, thick(), nolight); draw(shift(1,-1,0)*unitcube, white, thick(), nolight); draw(shift(1,0,-1)*unitcube, white, thick(), nolight); draw(shift(2,0,0)*unitcube, white, thick(), nolight); draw(shift(1,1,0)*unitcube, white, thick(), nolight); draw(shift(1,0,1)*unitcube, white, thick(), nolight);[/asy]](http://latex.artofproblemsolving.com/5/6/0/560b1370f7552768e471e84d48e042295acbc628.png)
Solution
The volume is of seven unit cubes which is 
. The surface area is the same for each of the protruding cubes which is 
. The ratio of the volume to the surface area is 
.
See Also
| 2008 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 15 |
Followed by Problem 17 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
