#### What is Volume?

When we talk about metric volume, we are talking about the amount of space and object takes up. Along with mass and length, volume is an important component in metric measurements. Examples of volume include:

- The volume of air in a room
- The volume of water in a swimming pool
- The volume of milk added to a recipe
- The volume of a soccer ball
- The volume of a solid block
- The volume of a human being

Notice in the examples above that volume does not refer only to empty containers but anything that takes up space. All matter has volume. Gases have volume (air in a room or in a soccer ball), liquids have volume (water in a pool, milk in a recipe) and solids have volume (building block, human being). Even the smallest and largest of objects have volume. Thus, a molecule has a volume as does a planet or star!

There are different kinds of volumes that we come in contact with in everyday life. We will learn more about three of them. These are regularly shaped solid volumes, irregularly shaped solid volumes and liquid volumes.

Regularly shaped volumes are composed of basic geometric shapes such as cylinders, spheres, and cubes or combinations of such regular shapes. Irregularly shaped volumes, on the other hand, are composed of complex combinations of non-regular shapes. Finally, there are liquid volumes that take the shapes of the contains in which they are placed.

- Look at the regularly and irregularly shaped objects in the picture above. Can you think of five more examples of regularly shaped volumes?
- Look at the regularly and irregularly shaped objects in the picture above. Can you think of five more examples of irregularly shaped volumes?
- Look at the liquid volumes in the picture above. Can you think of five more examples of liquid volumes?

#### LabLearner Tabs: Determining Volume From Dimensions

There are a number of common regular geometric shapes that we can calculate the volume of by their dimensions. We will consider four of them now – the cube, rectangular prism, the sphere, and the cylinder. Each of these shapes has a mathematical formula that allows us to calculate the volume based on measurements we can easily make with a metric ruler or meter stick.

- Volume from Dimensions
- Tab One: Determining the Volume of a Cube
- Tab Two: Determining the Volume of a Rectangular Prism
- Tab Three: Determining the volume of a Sphere
- Tab Four: Determining the Volume of a Cylinder

**Determining the Volume of a Cube**

There is a special kind of shape in which all three dimensions (length, width, and height) are the same. Such a shape is called a *cube*. Use this formula for the volume of a cube:

**V = s ^{3}** (s · s · s)

where: V=volume, s=side

Therefore, the volume of the example yellow cube above would be:

**V = s ^{3}**

**V = s · s · s**

**V = 3 cm · 3 cm · 3 cm = 27 cm ^{3}**

Notice that the final unit of volume is centimeters cubed (cm^{3}). This is because we multiplied cm times cm times cm, the three dimensions of the cube. The term *cubic* is always used to express volume. In this example, we would say that the cube has a volume of 27 cubic centimeters.

**Determining the Volume of a Rectangular Prism**

You can think of a rectangular prism as a three dimensional rectangle. It has three dimensions: length, width, and height. The volume of a rectangular prism is equal to its length (l) times its width (w) times its height (h). Use this formula:

**V = lwh**

Where: V = volume, l = length, w = width, h = height

We can calculate the volume of the blue rectangular prism above as follows:

**V = lwh**

**V = 1.5 cm x 3 cm x 9 cm = 40.5 cm ^{3}**

You can determine the volume of a room at your house by measuring its length, width, and hight from floor to ceiling.

**Determining the Volume of a Sphere**

You can think of a sphere as a three-dimensional volume based on a circle. We don’t talk about the height, width, or length of a sphere but rather refer to its circumference, diameter, or radius. Use this formula to calculate the volume of a sphere:

**V = ¾ π r ^{3}**

Where: V = volume, π = 3.14, r = radius

We can calculate the volume of the blue sphere above as follows:

**V = ¾ 3.14 (5 · 5 · 5)**

**= ¾ 3.14 x 125**

**= ¾ 392.5**

**= 1,77.5 cm ^{3} / 4**

**= 294.38 cm ^{3}**

Finally, finding the volume of a cylinder requires two measurements, its height and its radius. Use this formula:

**V = π r ^{2} h**

Where: V = volume, π = 3.14, r = radius, h = height

We can calculate the volume of the violet cylinder to the right as follows:

**V = π r ^{2} h**

**= 3.14 (1.5 cm x 1.5 cm) 6 cm**

**= 42.39 cm ^{3}**