Density, Area and Volume

Examples, solutions, videos, and lessons to help High School students learn how to apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).

Common Core: HSG-MG.A.2

The following diagram gives the Density-Mass-Volume formula. Scroll down the page for more examples and solutions.

 

Mass is a measure of the amount of matter in an object. We typically measure mass in units like grams (g) or kilograms (kg).
Volume is the amount of space that an object occupies. It is the three-dimensional space an object fills. Volume is commonly measured in cubic meters (m³), cubic centimeters (cm³), or for liquids, in liters (L).
Density is the relationship between an object’s mass and its volume. It tells us how tightly packed the matter is within an object. The unit for density is a combination of mass and volume units, such as grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).

Videos

Density, Mass and Volume
How to use the Density Mass Volume formula triangle and find volume of shapes. It goes through a couple of examples of finding mass.
Example:

1. The density of this metal block is 5 g/cm³. Find the mass of the block.
2. The density of this prism is 4 g/cm³. Find the mass of the prism.

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Density Word Problems
Simple problems dealing with density formula (D = m / v).
Example:

1. What is the density of an aluminum metal block that has a mass of 27.0 g and a volume of 10.0 cm³?
2. What is the density of a steel block that has a mass of 7.8 g and a volume of 1.0 cm³?
3. What is the density of a nail that has a mass of 12.5 g and a volume of 1.6 cm³?
4. On Great Skies Airlines a carry-on suitcase can be no more than 12 kg and 30,000 cm³. Does the following suitcase qualify as a carry-on.

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Density Calculations
Solving density word problems using the formula triangle.
Example:

1. A loaf of bread has a volume of 2,270 cm³ and a mass of 454 g. Whas the density of the bread?
2. What is the volume of a tank that can hold 18.754 g of methanol whose density is 0.788 g/cm³?
3. A bottle has a capacity of 1.2 liters. If the density of ether is 0.74 g/ml., what mass of ether can the bottle hold?

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Density Facts and Practice Problems
Learn more about density and practice calculating using word problems.
Density is how much mass is contained in a given volume?
Example:

1. What is the density of carbon dioxide gas if 0.196 g occupies a volume of 100 mL?
2. A block of wood 3 cm on each side has a mass of 27 g. What is the density of the block?
3. A 10.0 cm³ sample of copper has a mass of 89.6 g. What is the density of copper?

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Density Practice Problems
This video shows the equation for Density and gives 2 example problems.
Example:

1. What is the density of a bolt that has a mass of 14 g and a volume of 2 ml?
2. What is the volume of a liquid silver sample that has a density of 0.125 g/ml and a mass of 1.2g?

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What is BTU (British Thermal Unit)?
A short explanation of how to calculate water temperature rise in ц, given certain BTUs per hour.

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Understanding the BTU - Energy produced

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