## Mass Density

Density is the quantity of something proportional to the amount of space it takes up. For physical objects, it is an object's mass per unit of volume, usually expressed as grams per cubic centimeter (g/cm3) or kilograms per cubic meter (kg/m3). To calculate an object's density, divide its mass by its volume.
A luggage of clothes and other travel items has a mass of 18 kilograms, and a volume of 0.1 cubic meters. To calculate the density, do the following:
```mass    = 18 kilograms
volume  = 0.1 cubic meters
density = 18 kilograms ÷ 0.1 cubic meters = 180 kg/m3
```
A luggage that is empty has a mass of only 3.6 kilograms, but the same volume of 0.1 cubic meters. To calculate the density, do the following:
```mass    = 3.6 kilograms
volume  = 0.1 cubic meters
density = 3.6 kilograms ÷ 0.1 cubic meters = 36 kg/m3
```
A luggage that is full of bricks has an enormous mass of 180 kilograms, but the same volume of 0.1 cubic meters. To calculate the density, do the following:
```mass    = 180 kilograms
volume  = 0.1 cubic meters
density = 180 kilograms ÷ 0.1 cubic meters = 1,800 kg/m3
```
Density is the measure of how compact an object is. In the examples above, the luggage of clothes is 5 times more dense than the empty luggage, but 10 times less dense than the luggage of bricks.
Water has a density of 1 g/cm3 or 1,000 kg/m3. An object will float in water if it's less dense than water, and sink otherwise. In the examples above, both the luggage of clothes and empty luggage will easily float in water, but the luggage of bricks will sink.

### Exercise 1 of 6

A math textbook has a mass of 1,800 grams, and a volume of 2,400 cubic centimeters. How many g/cm3 is the density?

### Exercise 2 of 6

A gold bar has a mass of 12,545 grams, and a volume of 650 cubic centimeters. How many times more dense is the gold bar than water? Divide the density of the gold bar by the density of water.

### Exercise 3 of 6

A dry sponge has a mass of 25 grams, and a volume of 125 cubic centimeters. As the sponge absorbs water, its mass increases to 125 grams while maintaining the same volume. How many times more dense is the wet sponge than the dry sponge?

### Exercise 4 of 6

An inflated beach ball has a mass of 70 grams, and a volume of 35,000 cubic centimeters. A baseball has a mass of 140 grams, and a volume of 200 cubic centimeters. How many times more dense is the baseball than the inflated beach ball?

### Exercise 5 of 6

A scoop of vanilla ice cream has a mass of 100 grams, and a volume of 125 cubic centimeters. A cup of root beer has a mass of 364 grams, and a volume of 350 cubic centimeters. Will the ice cream float in the root beer?

### Exercise 6 of 6

Water is poured into an ice tray, and each slot holds 30 cubic centimeters of water. The ice tray is put into a freezer, and a few hours later, you take it out and find that each slot has an ice cube with a volume of 32.7 cubic centimeters. Will the ice cubes float in water?