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How to Find Volumetric Mass Density (Metric)

This entry uses the metric system. For the imperial system click here.

Mass density is a topic you may recognize from science class. The mass density of a substance says something about how compact a substance is. This means that you can have two objects that are the same size (volume), but due to different densities, one object will weigh more (have larger mass) than the other. Mass density is given by mass (m) divided by volume (V ). The symbol for mass density is the Greek letter ρ (rho).

Rule

Mass Density: Mass per Volume

ρ = m V

A scale with a leaf and a weight

Example 1

Iron has a mass density of ρ = 7.88g/cm3. An iron cannon ball has a volume of 1800cm3. What does the cannon ball weigh?

Insert the values into the formula and solve for m: ρ = m V m = ρ V = 7.88g/cm3 1800cm3 = 14184g 14kg

Mass density is measured in kg/m3, but there are also many other units in use. A unit you may have seen before, is g/cm3. Water has a mass density equal to 1g/cm3. If an object has a lower mass density than water, it will float in the water. However, if an object has a higher mass density than water, it will sink.

Example 2

A plank weighs 1500g, and has a volume of 2.75dm3. Will the plank float in water?

First, make sure the units are the same:

2.75dm3 = (2, 75 103)cm3 = 2750cm3

The plank has mass density

ρ = m V = 1500g 2750cm3 0.55g/cm3

The plank has a much lower mass density than water, which means it will float.

Example 3

Two gold bars

Annie has found two bars in a hidden cabinet. They are gold colored, and Annie wonders if she has found real gold bars, or if they have been painted on the outside. She has weighed and measured the volume of one of the bars. It weighed 12kg = 12000g, and had a volume of about 622cm3. Annie has found that the mass density of gold is 19.3g/cm3. Is it a real gold bar? ρ = m V = 12000g 622cm3 19.29g/cm3 19.3g/cm3

Annie’s bar definitely seems to be made of gold.

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