2010 AMC 10A Problem 12

Problem 12 of 25IntermediateAlgebra Geometry

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 miniature tower holds

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

times less water than the actual tower. Since this is the ratio for volumes, the ratio of heights is

(1,000,000)^{\frac{1}{3}} = 100.

This means that the height of the miniature tower is

\dfrac{40}{100} = 0.4.

Thus, C is the correct answer.