Question

A rock has a density of 4 g/mL and a mass of 16 grams. What is the volume this rock occupies?

Answer 1

`"4 mL"`

Explanation:

The density of the rock essentially tells you the mass of one unit of volume of that rock.

In this case, a density of `"4 g/mL"` means that `"1 mL"` of this rock, which would be a unit of volume when the volume is expressed in milliliters, has a mass of `"4 g"`.

You know that the rock has a mass of `"16 g"`. You can use the density of the rock

`"4 g/mL" = "4 grams"/"1 mL"`

as a conversion factor to help you figure out its volume.

To do that, rearrange the density to have the mass as the denominator and the volume as the numerator and multiply the resulting fraction by the mass of the rock.

You will have

`16 color(red)(cancel(color(black)("g"))) * "1 mL"/(4color(red)(cancel(color(black)("g")))) = color(green)(bar(ul(|color(white)(a/a)color(black)("4 mL")color(white)(a/a)|)))`

The answer is rounded to one sig fig.