Question

the scale for a certain model freight train is 1: 48. if the model hopper car (usually used for carrying coal) will hold 90 in3 of coal, what is the capacity of the actual hopper car?​

Answer 1

Explanation:

Scale measure is a one-to-one thing while volume is a cubed thing. If we want to find the volume that the actual car can hold, we have to find the volume that results from cubing the one-to-one measure.

`(m)/(a):(1^3)/(48^3)=(1)/(110592)` That last fraction is the ratio of the volumes. Remember, volume is a cubed measure (where distance is a linear measure and area is a squared measure. We find ratios of areas by squaring the one-to-one {distance} measures, and we find ratios of volumes by cubing the one-to-one measures). We have a given volume for the model (m in our ratio) and we are looking for the capacity that the actual car (a in our ratio) can hold. Set up the proportion as follows:

`(1)/(110592)=(90)/(x)` and cross multiply

x = 9,953,280 inches cubed