Question #ad05a

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"#