Question #337cb

1 Answer
Feb 24, 2018

Answer:

#"55 cm"^3#

Explanation:

The thing to remember about the density of a given substance is that it tells you the mass of exactly #1# unit of volume of that substance.

In your case, you know that the density of steel is equal to #"7.8 g cm"^(-3)#. This value tells you that every #"1 cm"^3# of steel, the equivalent of one unit of volume, has a mass of #"7.8 g"#.

So if you know that you need #"7.8 g"# of steel in order to have #"1 cm"^3# of steel, you can say that #"430 g"# of steel would correspond to a volume of

#430 color(red)(cancel(color(black)("g"))) * "1 cm"^3/(7.8color(red)(cancel(color(black)("g")))) = color(darkgreen)(ul(color(black)("55 cm"^3)))#

The answer is rounded to two sig figs.

So remember, every time you have the density of a substance, you can use it as a conversion factor to find the mass of a given volume or the volume of a given mass.

For this example, you would have

#"mass " -> " volume:" " " "1 cm"^3/"7.8 g"#

#"volume " -> " mass:" " " "7.8 g"/"1 cm"^3#