Question

A coffee cup is found to have a volume of 0.238 liters. How do you calculate, using unit analysis, the volume of the coffee cup, in gallons?

Answer 1

`0.238` `"L"` `= color(red)(0.0629` `color(red)("gal"`

Explanation:

Using dimensional analysis, we can multiply the known value by a conversion factor to convert to a new unit while canceling the old one.

The known value here is

`0.238` `"L"`

The conversion factor is

`1` `"gal"` `= 3.785` `"L"`

which we can also write as

`(1color(white)(l)"gal")/(3.785color(white)(l)"L")`

We multiply the conversion factor by the known value so that the units cancel out algebraically and you're left with the desired unit. It looks like this:

`0.238cancel("L")((1color(white)(l)"gal")/(3.785cancel("L"))) = color(red)(0.0629` `color(red)("gal"`

Therefore, `0.238` `"L"` is equal to

`color(red)(ul(0.0629color(white)(l)"gal"))`