Question

A loaf of bread has a volume of `"2270 cm"^3` and a mass of `"454 g"`. What is the density of the bread?

Answer 1

`"0.200 g cm"^(-3)`

Explanation:

The idea here is that the density of the loaf of bread will tell you the mass of exactly `1` unit of volume of bread, i.e. of `"1 cm"^3` of bread.

In your case, the loaf of bread is said to have a volume of `"2270 cm"^3` and a mass of `"454 g"`. In order to find the density of the bread, you must figure out the mass of `"1 cm"^3` of bread.

To do that, you can use the mass and the volume of the loaf of bread as a conversion factor.

`1 color(red)(cancel(color(black)("1 cm"^3))) * "454 g"/(2270 color(red)(cancel(color(black)("1 cm"^3)))) = "0.200 g"`

So if `"1 cm"^3` of bread has a mass of `"0.200 g"`, you can say that the density of the loaf of bread is

`color(darkgreen)(ul(color(black)("density = 0.200 g cm"^(-3)))`

The answer is rounded to three sig figs, the number of sig gigs you have for your values.

Notice that you can get the same answer by dividing the total mass of the loaf of bread by the total volume it occupies.

`"density" = "454 g"/"2270 cm"^3 = 454/2270 quad "g"/"cm"^3 = "0.200 g cm"^(-3)`