Question

Question #8d973

Answer 1

`"75 cm"^3` of iron.

Explanation:

Your tools of choice here will be the densities of the two elements, which you'll find listed as

• `rho_"Fe" = "7.874 g cm"^(-3) ->` source
• `rho_"Al" = "2.70 g cm"^(-3) ->` source

Keep in mind that the two densities are cited for room temperature, which implies that you're dealing with solid iron and solid aluminium.

Now, the density of a substance tells you the mass of exactly `1` unit of volume that substance occupies.

In your case, you know that `"1 cm"^3` of iron has a mass of `"7.784 g"` and `"1 cm"^3` of aluminium has a mass of `"2.70 g"`.

This means that your two samples will have masses of

`75 color(red)(cancel(color(black)("cm"^3))) * overbrace("7.784 g"/(1color(red)(cancel(color(black)("cm"^3)))))^(color(blue)("the density of iron")) = "584 g"`

`100color(red)(cancel(color(black)("cm"^3))) * overbrace("2.70 g"/(1color(red)(cancel(color(black)("cm"^3)))))^(color(blue)("the density of aluminium")) = "270 g"`

As you can see, `"75 cm"^3` of iron will have a greater mass than `"100 cm"^3` of aluminium.