Difference between revisions of "2010 AMC 10A Problems/Problem 12"

Latest revision as of 16:44, 17 January 2016

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-== Problem ==
+#REDIRECT [[2010_AMC_12A_Problems/Problem_7]]
-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?
-<math>\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</math>
-== 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>.
-== See also ==
-{{AMC10 box|year=2010|num-b=11|num-a=13|ab=A}}