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?

Answer 1

0.4 m = 40 cm

Explanation:

You want the height of a model water tower with a volume of 0.1 liters that models a city water tower 40 m high with a volume of 100,000 liters.

Scale factor

The scale factor for volume is the cube of the scale factor for linear dimensions, such as height. Conversely, the scale factor for height is the cube root of the scale factor for volume.

This lets us write a proportion for the height of the model tower:

`\frac{h}{40\text{ m}}=\sqrt[3]{\frac{0.1\text{ L}}{100000\text{ L}}}\\\\h=(40\text{ m})\sqrt[3]{10^(-6)}=\boxed{0.40\text{ m}}`

Logan should make his tower 0.4 meters, or 40 cm high.