Question #69959

2 Answers
Sep 9, 2016

Answer:

The brick.

Explanation:

Density is simply a measure of how heavy a unit of volume of a given substance is.

In this regard, the density of a substance is equivalent to the mass of exactly #"1 mL"# or #"1 cm"^3# of that substance.

In your case, you must find the substance that has the greatest mass for a given volume, let's say #V# #"mL"#. You know that you're dealing with

  • a brick that has a density of #"1.41 g/mL"#
  • ice, which has a density of #"0.92 g/mL"#
  • liquid water, which has a density of #"1.00 g/mL"#
  • wax, which has a density of #"0.79 g/mL"#

What this tells you is that for #"1 mL"# of these substances, you get

  • the brick: #"1.41 g"#
  • ice: #"0.92 g"#
  • liquid water: #"1.00 g"#
  • wax: #"0.79 g"#

If equal volumes of these substances are compared, you can be certain that the substance that has the greatest mass for #"1 mL"#, i.e. the highest density, will have the greatest mass.

In this case, the brick will "win" because it is the heaviest of the three substances when comparing equal volumes.

#V color(red)(cancel(color(black)("mL"))) * "1.41 g"/(1color(red)(cancel(color(black)("mL")))) = (1.41 * V)" g " -># the brick

#V color(red)(cancel(color(black)("mL"))) * "0.92 g"/(1color(red)(cancel(color(black)("mL")))) = (0.92 * V)" g " -># ice

#V color(red)(cancel(color(black)("mL"))) * "1.00 g"/(1color(red)(cancel(color(black)("mL")))) = (1.00 * V)" g " -># liquid water

#V color(red)(cancel(color(black)("mL"))) * "0.79 g"/(1color(red)(cancel(color(black)("mL")))) = (0.79 * V)" g " -># wax

As you can see, when #V# is the same for all four substances, the brick will always have the greatest mass because it has the highest density.

Sep 9, 2016

Answer:

There's an even easier way to visualise it.....

Explanation:

If you say density = d, mass =m and volme=v:

#d = m/v#

so: #m = v.d#

and we know v will be constant, so its easy to see that mass varies directly with density for a constant volume.

On that basis, the one with the largest mass will be that one with the largest density. Which is the brick.

Simple!