Question

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?

$0.04$

$\dfrac{0.4}{\pi}$

$0.4$

$\dfrac{4}{\pi}$

$4$

Answer: C

Concepts:power scaling of length, area, and volume volume

Difficulty rating: 1420

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.

2010 AMC 12A Problem 7

Answer: C

Difficulty rating: 1420

Solution:

Problem 7 in Other Years