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How to Find Volumetric Mass Density (Imperial)

This entry uses the imperial system of measurement. It is more common to use the metric system when you measure density. Click here to go to the metric version of this page.

I choose to use lb/ft3 for this page.

Mass density is a topic you may recognize from science class. The 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 density of ρ = 7.88lb/ft3. An iron cannon ball has a volume 1800ft3. What does the cannon ball weigh?

Insert into the formula and solve for m: ρ = m V m = ρ V = 7.88lb/ft3 1800ft3 = 14184lb = 7.092 short ton

Water has a mass density equal to 62.4lb/ft3. If an object has a lower density than water, it will float on the water. However, if an object has a higher mass density than water, it will sink.

Example 2

A plank weighs 1lb, and has volume 600in3. Will the plank float on the water?

First, make sure the units are the same. Since one foot is 16 inches, 1ft3 = 16 16 16 = 1728in3. This means you need to divide the in3 by 1728

600in3 = 600 1728ft3 0.347ft3

The plank has density

ρ = m V = 1lb 0.347ft3 2.857lb/ft3.

The plank has a much lower density than water, and will thus float.

Example 3

Two bars of gold

Annie has found two bars in a hidden cabin. They are gold colored, and Annie wonders if she has found real gold bars, or if they are only painted on the outside. She has weighed and measured the volume of one of the bars. It weighed 26.5lb, and had a volume of about 0.022ft3. Annie has found that the mass density of gold is around 1206.11lb/ft3. Is it a real gold bar? ρ = m V = 26.54lb 0.022ft3 1206.37lb/ft3 1206.11lb/ft3

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

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