Question

Question #ad05a

Answer 1

Here's what I got.

Explanation:

I'm assuming that you're starting with a piece of iron that has a known volume and are interested in finding its mass in pounds.

The thing to keep in mind density is that it can be used as a conversion factor to help you go from mass to volume or vice versa.

Let's say that in your case, you have a piece of iron of volume `V` `"cm"^3`. The density of iron is said to be equal to `"7.9 g cm"^(-3)`. This tells you that `"1 cm"^3` of iron has a mass of `"7.9 g"`.

As a result, the piece of iron of volume `V` will have a mass of

`V color(red)(cancel(color(black)("cm"^3))) * overbrace("7.9 g"/(1color(red)(cancel(color(black)("cm"^3)))))^(color(blue)("the given density")) = (7.9 * V)" g"`

Now all you have to do is use the given conversion factor

`color(purple)(|bar(ul(color(white)(a/a)color(black)("1 lb " = " 453.6 g")color(white)(a/a)|)))`

to convert the mass from grams to pounds

`(7.9 * V) color(red)(cancel(color(black)("g"))) * "1 lb"/(453.6color(red)(cancel(color(black)("g")))) = (0.0174 * V)" lb"`

As a numerical example, let's say that `V = "122 cm"^3`. The mass in pounds of this volume of iron will be

`"mass in lb" = 0.0174 * 122 = "2.12 lb"`