Question

Question #46628

Answer 1

`"$532,000"`

Explanation:

The first thing that you should know here is that

`color(blue)(ul(color(black)("1 mL" = "1 cm"^3)))`

This means that you can express the volume of the can as

`"355 mL" = "355 cm"^3`

Now, the density of platinum tells you the mass of exactly `"1 cm"^3` of platinum. In this case, you know that every `"1 cm"^3` of platinum has a mass of `"21.4 g"`.

You can thus use the density of platinum as a conversion factor to determine the mass of platinum present in the sample.

`355 color(red)(cancel(color(black)("cm"^3))) * overbrace("21.4 g"/(1color(red)(cancel(color(black)("cm"^3)))))^(color(blue)("the density of platinum")) = "7,597 g"`

Finally, you know that you can get `$70.00` per gram of platinum, which means that the sample will have a value of

`"7,597" color(red)(cancel(color(black)("g"))) * ($70.00)/(1color(red)(cancel(color(black)("g")))) = color(darkgreen)(ul(color(black)("$532,000")))`

The answer is rounded to three sig figs, the number of sig figs you have for the volume of the can.