All objects have mass. Mass is the amount of material in an object, usually measured by its weight. Earlier in this unit, you studied the volume of objects. When you combine these two concepts, you get a useful measurement called density. The density of an object is its mass per unit of volume. Imagine two objects in which the larger one actually weighs less than the smaller one. This difference in weight is attributed to density.

Consider a candle that has a volume of 96 cubic inches and a weight of 44.16 ounces. What is the density of the candle? The density is defined as its mass per unit volume, so simply divide the mass of the candle by its volume:

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In this case, you are finding the average density of the candle. In most cases, you will be finding the average density of objects because most objects do not have a uniform density. For instance, the portion of the candle where the wick is might have a different density than the rest of the candle.

Now that you know about density, let’s work on some applications.

Harold is a woodworker and is interested in finding the density of two different types of wood. He bought a pine log that has a 5-inch radius and is 30 inches long. The weight of the log is approximately 42.63 pounds. He also has an oak board that is 5.5 inches wide, 1.5 inches thick and 3 feet long. The board weighs approximately 8.05 pounds.

Part A
Which shapes can you use to model the log and the board?

Part B
What is the density of the pine log? Show your work.

Part C
What is the density of the oak board? Show your work.

Part D
If you had a block of each type of wood with the same dimensions, how would their weights compare? Explain.

Part E
Water has a density of about 0.0361 pounds/cubic inch. You might know that wood floats on water. What can you conclude about the densities of objects that float and the densities of objects that do not? Review your results from parts B and C before deciding.