Question

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:
.

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.

1. What Is the density of the pine log?....
2.What is the density of the oak board?....
3.If you had a block of each type of wood with the same dimensions, how would their weights compare? Explain....

Answer 1

Answer:

1. 55.271 inches/lb

2. 3.075 inches/lb

3. The denser one is the pine, so it would be heavier.

Step-by-step explanation:

1. density of the pine log (which is a cylinder)

    We need the weight/mass and the volume.

    V(cylinder) = πr^2 * height

                       =  πr^2 = π(5^2) = 25π = 78.54

                       = 78.54 * 30 = 2356 cubic inches

    The weight is 42.63.

  Density = mass/volume = 2356/42.63 = 55.271 inches/lb

2. density of the oak board (which is a rectangular prism)

    We need the weight/mass and the volume.

    V(prism) = l*w*h

                   = 5.5*1.5*3 = 24.75 cubic inches

    The weight is 8.05.

  Density = mass/volume = 24.75/8.05 = 3.075 inches/lb

3. Picture a box made out of stone and a box made out of cardboard. Same dimensions, but the stone one would be way heavier because stone is denser.