While on a social studies class trip to the museum, Maurice and Timothy were admiring the tall columns in one of the museum’s galleries. The six circular columns extended from their flat base on the floor 12 feet upward to the ceiling. Maurice believed the columns were prisms, while Timothy argued that they were cylinders. Who was right?

In this concept, you will learn to classify solid figures.

### Classifying Solid Figures

Figures can be classified according to their dimensions. Two-dimensional figures are **plane figures**, or “flat” figures. A **plane figure** is a flat figure that does not have depth to it.

Here are some examples of plane figures.

Here you have a circle, a triangle and a rectangle. You can see that these figures have been created on one plane. They are two-dimensional figures.

Then, there are three-dimensional figures or **solid figures**. **Solid figures** are not limited to one plane and have depth. There are many different types of solid figures.

Let’s take a look at a few solid figures.

A **prism** is a figure that has two parallel congruent bases. The bases can be any polygon. Here is an example of a familiar prism.

This is a cube. A cube is a type of prism. Notice that the two bases of the cube are squares. One is on the top and the other is on the bottom.

Prisms are classified and named by the number of sides and flat planes in the solid figure. Here are some common prisms.

Triangular prisms – 3 sides or flat planes

Rectangular prisms and Cubes – 4 sides or flat planes

Pentagonal prisms – 5 sides or flat planes

Hexagonal prisms – 6 sides or flat planes

**Cylinders** are common in everyday life as well. A cylinder has two bases that are circles. A rectangle is wrapped around the bases forming the center. Here is an image of a cylinder.

A **pyramid** has one polygon as a base and sides that are triangular faces and connect in one vertex at the top.

A **cone** has one circular base and the sides of the cone meet in one vertex at the top. The sides are one piece that is wrapped around the circular base forming a single vertex.

A **sphere** has a set of connected points located around one center point. While circular in form, it is also three dimensional. An example of a sphere is a baseball.

### Examples

#### Example 1

Earlier, you were given a problem about Maurice and Timothy’s debate about the columns at the museum.

Maurice believed the columns were prisms because they had two flat bases that were congruent to each other. Timothy agreed with Maurice about the two flat bases but insisted that, because the bases were circles and the columns didn’t have any flat planes, they were cylinders.

First, recall the definition of both prisms and cylinders as you look at the column below.

Prisms have two flat, congruent bases and sides that are flat planes. Cylinders have two flat, congruent bases that are circles and no flat planes for sides.

The columns had bases that were circles and no flat planes for sides, so the columns were cylinders.

The answer is Timothy is right – the columns are cylinders.

#### Example 2

Identify the solid figure displayed here.

First, identify the object.

It is a box and has two congruent bases. Looking at the edges, the box has rectangular faces because the length and width of the sides are not equal.

Next, identify the type of solid figures that have congruent bases and rectangular faces.

The answer is a prism.

#### Example 3

Identify the solid figure.

First, identify the shape and any flat planes the object has.

This object has a circular shape with two flat bases.

The answer is it is a cylinder.

#### Example 4

Identify the solid figure.

First, identify the shape and any flat planes the object has.

This object is circular and has no flat planes or edges.

The answer is it is a sphere.

#### Example 5

Identify the solid figure.

First, identify the shape and any flat planes the object has.

It is shaped like a square and has 6 flat planes – 2 congruent bases and 4 faces.

The answer is a cube.

### Review

Look at each figure or picture and determine whether each is a prism, pyramid, cylinder, cone or sphere.

Name each type of prism.

### Review (Answers)

To see the Review answers, open this PDF file and look for section 10.12.