Difference between revisions of "2010 AMC 12A Problems/Problem 7"

Revision as of 21:46, 3 July 2013

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?

$\textbf{(A)}\ 0.04 \qquad \textbf{(B)}\ \frac{0.4}{\pi} \qquad \textbf{(C)}\ 0.4 \qquad \textbf{(D)}\ \frac{4}{\pi} \qquad \textbf{(E)}\ 4$

Solution

The water tower holds $\frac{100000}{0.1} = 1000000$ times more water than Logan's miniature. Therefore, Logan should make his tower $\sqrt[3]{1000000} = 100$ times shorter than the actual tower. This is $\frac{40}{100} = \boxed{0.4}$ meters high, or choice $\textbf{(C)}$ .

Also, the fact that $1 L=1dm^3$ doesn't matter since only the ratios are important.

2010 AMC 12A (Problems • Answer Key • Resources)
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All AMC 12 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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 [[Category:Introductory Geometry Problems]]
 [[Category:3D Geometry Problems]]
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Difference between revisions of "2010 AMC 12A Problems/Problem 7"

Revision as of 21:46, 3 July 2013

Problem

Solution

See also