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Difference between revisions of "2008 AMC 8 Problems/Problem 16"

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==Solution==
 
==Solution==
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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 5*6=30 The ratio of the volume to the surface area is D
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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{\text{(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}}
 
{{MAA Notice}}

Revision as of 18:24, 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]

$\textbf{(A)} \:1 : 6 \qquad\textbf{ (B)}\: 7 : 36 \qquad\textbf{(C)}\: 1 : 5 \qquad\textbf{(D)}\: 7 : 30\qquad\textbf{ (E)}\: 6 : 25$

Solution

The volume is of seven unit cubes which is $7$. The surface area is the same for each of the protruding cubes which is $5\cdot 6=30$. The ratio of the volume to the surface area is $\boxed{\text{(D)}\ 7:30}$.

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

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