Question

I want to find the volume of a grain bin and I am trying to use this formula:

Volume = 1#(15 ft)² × (3 ft) + 7(15 ft)(22 ft). Clearly explain how you can tell this is wrong without knowing any volume formulas (hint: units).

Answer 1

The given formula for volume is incorrect because it contains a term with squared units, indicating area, rather than cubic units, which are necessary for expressing volume.

Step-by-step explanation:

We can tell the given formula for the volume of a grain bin is wrong by examining the units. In the correct volume formula, all the terms on the right side must multiply to give a result in cubic units (like cubic feet or cubic meters), since volume is a measure of three-dimensional space. However, the given formula has terms that result in units that are not cubic. For example, the term 1#(15 ft)² × (3 ft) would result in squared units multiplied by linear units, giving cubic units, which is correct for volume. On the other hand, the term 7(15 ft)(22 ft) only gives squared units, which corresponds to area and not volume. We expect a formula for volume to only have terms that result in cubic units.