Density is the amount of matter, or mass, per unit volume. This example problem shows how to calculate the mass of an object from a known density and volume.
The density of gold is 19.3 grams per cubic centimeter. What is the mass of a bar of gold in kilograms that measures 6 inches x 4 inches x 2 inches?
Density is equal to the mass divided by the volume.
D = m/V
D = density
m = mass
V = volume
We have the density and enough information to find the volume in the problem. All that remains is to find the mass. Multiply both sides of this equation by the volume, V and get:
m = DV
Now we need to find the volume of the gold bar. The density we have been given is in grams per cubic centimeter but the bar is measured in inches. First we must convert the inch measurements to centimeters.
Use the conversion factor of 1 inch = 2.54 centimeters.
6 inches = 6 inches x 2.54 cm/1 inch = 15.24 cm.
4 inches = 4 inches x 2.54 cm/1 inch = 10.16 cm.
2 inches = 2 inches x 2.54 cm/1 inch = 5.08 cm.
Multiply all three of these numbers together to get the volume of the gold bar.
V = 15.24 cm x 10.16 cm x 5.08 cm
V = 786.58 cm3
Place this into the formula above:
m = DV
m = 19.3 g/cm3 x 786.58 cm3
m = 14833.59 grams
The answer we want is the mass of the gold bar in kilograms. There are 1000 grams in 1 kilogram, so:
mass in kg = mass in g x 1 kg/1000 g
mass in kg = 14833.59 g x 1 kg/1000 g
mass in kg = 14.83 kg.
The mass of the gold bar in kilograms measuring 6 inches x 4 inches x 2 inches is 14.83 kilograms.
For more example problems, use the Worked Chemistry Problems. It contains over a hundred different worked example problems useful for chemistry students.
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