# 10.1: Classification of Solid Figures

**At Grade**Created by: CK-12

Candice and Trevor have gotten a job working at the mall for the holiday season. They are both going to be working in the wrapping station. During the holidays, the mall offers free gift wrapping. People can come through and have their gifts wrapped. If they want to make a donation they can and that money is used to help needy families.

Candice and Trevor both show up on their first day for training. Mrs. Scott, the manager of the wrapping station shows them both where they will be working.

“First, we need to show you some great techniques for wrapping presents,” Mrs. Scott explains. “There are some ways that are more effective and useful than others.”

Candice and Trevor both take a seat in front of a bunch of different items.

There is a round bottle of perfume, a shoe box, a soccer ball and a magician’s hat with a round bottom and a point at the top.

“What kinds of shapes to do you see here?” Mrs. Scott asked the two.

**Before seeing Candice and Trevor’s answers, think about this question yourself. Based on the descriptions, how would you classify these objects? Make a few notes in your notebook.**

**In this Concept, you will learn how to classify three-dimensional solids. By the end of this Concept, you will know how Candice and Trevor can classify each item.**

### Guidance

In our earlier Concepts, all of the figures that we have been working with have been ** plane figures** which are

**two-dimensional figures**. This means that they have only length and width. Even a circle which has a circumference and a diameter is still a plane figure. It does not have depth.

This lesson will focus on ** solid figures** and solid figures are

**three-dimensional figures**.

**How is a solid figure different from a plane figure?**

**A** *solid figure***has length, width and height,** whereas a plane figure only has length and width.

Let’s look at some plane figures.

Now let’s look at some solid figures.

We see solid figures around us every day. Take a look around you. What solids do you see? How many faces or edges do they have? Recognizing and understanding these figures is an important key to doing geometry.

**How can we identify different solid figures?**

We can identify them according to the features that are unique to each type of solid.

**A** *sphere***is a solid figure that has no faces, edges, or vertices. This is because it is completely round; it has no flat sides or corners.**

**A** *cone***has one face but no edges or vertices. Its face is in the shape of a circle.** Because a circle is a flat, plane shape, it is a face. But because it is round around the outside, it does not form any edges or vertices. You will learn more about those in a minute.

**A** *cylinder***has two circular faces but also no edges or vertices.**

*Pyramids***have one base and at least three triangular sides.** A triangular pyramid has a triangular base and three other triangular faces, or four in all. A rectangular pyramid has a rectangular base and four other triangular faces, or five in all. It has edges and vertices where all of its faces meet, and always has a vertex at the top.

**A** *prism***is a solid figure that has two congruent parallel bases and any number of sides.** In other words, it can have any number of faces, but at least two of them must be parallel. The shape of the two parallel bases can be a triangle, square, rectangle, pentagon, hexagon, or any other kind of polygon. The number of sides the bases have determines the number of faces the figure has. The number of edges and vertices also depends on the shape of the base. Here are some different prisms.

As you can see, there are many types of prisms. The shape of the bases tells us which kind of prism it is.

Identify each solid figure. Be as specific as you can.

#### Example A

**Solution: Pentagonal Prism**

#### Example B

**Solution: Triangular Pyramid**

#### Example C

**Solution: Cone**

Here is the original problem once again.

Candice and Trevor have gotten a job working at the mall for the holiday season. They are both going to be working in the wrapping station. During the holidays, the mall offers free gift wrapping. People can come through and have their gifts wrapped. If they want to make a donation they can and that money is used to help needy families.

Candice and Trevor both show up on their first day for training. Mrs. Scott, the manager of the wrapping station shows them both where they will be working.

“First, we need to show you some great techniques for wrapping presents,” Mrs. Scott explains. “There are some ways that are more effective and useful than others.”

Candice and Trevor both take a seat in front of a bunch of different items.

There is a round bottle of perfume, a shoe box, a soccer ball and a magician’s hat with a round bottom and a point at the top.

“What kinds of shapes to do you see here?” Mrs. Scott asked the two.

**As Trevor and Candice tell Mrs. Scott what types of figures are present on the table, let’s do our own inventory.**

**The round bottle of perfume is a cylinder.**

**The shoe box is a rectangular prism.**

**The soccer ball is a sphere.**

**The magician’s hat is in the shape of a cone.**

**How did you do? Go back and check the answers that you wrote at the beginning of the lesson. If you got them all correct, good work. If not, then make a note of which ones you mixed up to help yourself next time.**

### Vocabulary

Here are the vocabulary words that are found in this Concept.

- Plane figure
- a two-dimensional figure

- Solid figure
- a three-dimensional figure

- Face
- the flat polygon of a solid figure. A figure can have more than one face.

- Prism
- a three-dimensional figure with two parallel congruent polygons as bases

- Pyramid
- a three-dimensional figure with one polygon for a base and all faces meet at one vertex.

### Guided Practice

Here is one for you to try on your own.

What is the name of this figure? Be as specific as you can.

**Answer**

This figure is a rectangular prism.

### Video Review

Here is a video for review.

- This is a video on the properties of solid figures.

### Practice

Directions: Identify each figure. Be as specific as possible.

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

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### Image Attributions

Here you'll learn to classify solid figures as prisms, cylinders, pyramids, cones or spheres.