# Question 69959

Sep 9, 2016

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 $\text{1 mL}$ or ${\text{1 cm}}^{3}$ of that substance.

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

• a brick that has a density of $\text{1.41 g/mL}$
• ice, which has a density of $\text{0.92 g/mL}$
• liquid water, which has a density of $\text{1.00 g/mL}$
• wax, which has a density of $\text{0.79 g/mL}$

What this tells you is that for $\text{1 mL}$ of these substances, you get

• the brick: $\text{1.41 g}$
• ice: $\text{0.92 g}$
• liquid water: $\text{1.00 g}$
• wax: $\text{0.79 g}$

If equal volumes of these substances are compared, you can be certain that the substance that has the greatest mass for $\text{1 mL}$, 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

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

#### Explanation:

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

$d = \frac{m}{v}$

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!