Question

What is the mass of a piece of metal that raises the volume of water in a graduated cylinder from `"15.0 cm"^3` to `"70.0 cm"^3` ? the density of iron is `"5.1 g/cm"^3`

Answer 1

`"281 g"`

Explanation:

The idea here is that the volume of the metal will cause the volume of the water to increase from its initial value of `"15.0 cm"^3` to the final value of `"70.0 cm"^3`.

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In other words, the difference between the final volume of the water, i.e. the volume of the water + metal, and the initial volume of the water will give you the volume of the metal

`V_"metal" = "70.0 cm"^3 - "15.0 cm"^3 = "55.0 cm"^3`

Now, the problem tells you the metal has a density of `"5.1 g cm"^(-3)`. This means that every cubic centimeter of this metal has a mass of `"5.1 g"`.

In your case, `"55.0 cm"^3` will have a mass of

`55.0 color(red)(cancel(color(black)("cm"^3))) * overbrace("5.1 g"/(1color(red)(cancel(color(black)("cm"^3)))))^(color(purple)("given density")) = color(green)(|bar(ul(color(white)(a/a)color(black)("281 g")color(white)(a/a)|)))`

I'll leave the answer rounded to three sig figs.