Question

A block of platinum with a mass of 4,290 kilograms has a volume of .2 cubic meters. What is the density of platinum in kilograms per cubic meter?

Answer 1

`"21,450 kg/m"^3`

Explanation:

Your goal when dealing with density problems is to figure out the mass of one unit of volume.

In this case, volume is given to you in cubic meters, `"m"^3`, which means that your goal is to find the mass of `"1 m"^3` of platinum.

How do you do that?

Notice that the problem tells you that a volume of `"0.2 m"^3` has a mass of `"4,290 kg"`. Since density is essentially a measure of how the atoms of an element pack per unit of volume, you can say that the same mass will always correspond to the same volume.

This means that if `"0.2 m"^3` have a mass of `"4,290 kg"`, then `"0.4 m"^3` will have a mass of `(2 xx "4,290 kg")`, `"0.6 m"^3` will have a mass of `(3 xx "4,290 kg")`, and so on.

Simply put, the mass of one cubic meter will be

`1 color(red)(cancel(color(black)("m"^3))) * "4,290 kg"/(0.2color(red)(cancel(color(black)("m"^3)))) = "21,450 kg"`

Therefore, you can say that platinum has a density of `"21,450 kg/m"^3`, meaning that every `'m"^3` of platinum has a mass of `"21,450 kg"`.