Applying Density to Real-Life Situations

Density is described as mass per unit volume. The formula for density is below:

$LaTeX: Density=\frac{mass}{volume}\:or\:D=\frac{m}{v}$

Check out this video for more on volume and density calculations!

Let's try one more example together:

You decide to buy your best friend a helium balloon for her birthday. The density of helium is about 0.18 kilograms per cubic meter. The volume of the balloon you purchase is 4 cubic meters. How many kilograms of helium does the balloon hold?

We know the formula for density is equation image indicator $LaTeX: density\:=\frac{\:mass}{volume}$

Here, we know the density and the volume, and we want to find the mass. So we simply plug in our known values and solve for the unknown!

$LaTeX: 0.18\:=\frac{\:mass}{4}$

(0.18)(4) = mass

0.72 kilograms = mass

So the balloon holds 0.72 kilograms of helium.

We can generalize the concept of density of something as "how much per unit" - this allows us to think of population density; for example, how many people live in one square mile? This conceptualization of density allows us to think outside of the strict lines of the formula and to develop a broader meaning of density that can be applied to situations where we may not have mass and volume.

For example, the population of Atlanta is approximately 450,000 people. The area of Atlanta is 132.4 square miles. Thus, the population density (people per square mile) would be calculated:

$LaTeX: D\:=\frac{\:450,000\:people\:}{132.4\:square\:miles}$

This simplifies to

$LaTeX: D\:=3398.8\frac{\:people}{square\:mile}$

Try your hand at some practice problems below!

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