2010 AMC 12A Problem 7

Problem 7 of 25EasierGeometry

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?

Show solution

Solution

The model-to-original volume ratio is

\dfrac{0.1}{100{,}000}=\dfrac{1}{1{,}000{,}000}.

Lengths scale by the cube root, so the model-to-original height ratio is

\dfrac1{100}.

Therefore the model should be

\dfrac{40}{100}=0.4

meters tall. Thus, C is the correct answer.