Difference between revisions of "2010 AMC 12A Problems/Problem 7"
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== Solution == | == Solution == | ||
The water tower holds <math>\frac{100000}{0.1} = 1000000</math> times more water than Logan's miniature. Therefore, Logan should make his tower <math>\sqrt[3]{1000000} = 100</math> times shorter than the actual tower. This is <math>\frac{40}{100} = \boxed{0.4}</math> meters high, or choice <math>\textbf{(C)}</math>. | The water tower holds <math>\frac{100000}{0.1} = 1000000</math> times more water than Logan's miniature. Therefore, Logan should make his tower <math>\sqrt[3]{1000000} = 100</math> times shorter than the actual tower. This is <math>\frac{40}{100} = \boxed{0.4}</math> meters high, or choice <math>\textbf{(C)}</math>. | ||
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| + | Also, the fact that <math>1 L=1dm^3</math> doesn't matter since only the ratios are important. | ||
== See also == | == See also == | ||
{{AMC12 box|year=2010|num-b=6|num-a=8|ab=A}} | {{AMC12 box|year=2010|num-b=6|num-a=8|ab=A}} | ||
Revision as of 09:02, 5 August 2012
Problem
Logan is constructing a scaled model of his town. The city's water tower stands 40 meters high, and the top portion is a sphere that holds 100,000 liters of water. Logan's miniature water tower holds 0.1 liters. How tall, in meters, should Logan make his tower?
Solution
The water tower holds 
times more water than Logan's miniature. Therefore, Logan should make his tower ![$\sqrt[3]{1000000} = 100$](http://latex.artofproblemsolving.com/7/0/5/7059c25b41a49aadf0f433430eb36aeb9ce89dc2.png)
times shorter than the actual tower. This is 
meters high, or choice 
.
Also, the fact that 
doesn't matter since only the ratios are important.
See also
| 2010 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 6 |
Followed by Problem 8 |
| 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 AMC 12 Problems and Solutions | |
