# 10.12: Classification of Solid Figures

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

**Practice**Classification of Solid Figures

Have you ever tried to make something by following a pattern? Take a look at this dilemma.

“My goodness Jillian, your quilting things are all over the place,” Jillian’s mother said to her one afternoon.

Jillian looked around the room. It was definitely true. Her supplies were everywhere.

“Maybe you should make a sewing box for yourself,” her mother suggested. “I have a pattern in a craft magazine that I have been reading and you can make it yourself.”

“That’s a great idea, thanks mom,” Jillian said, taking the magazine from her mother.

Jillian read the article on making the box and began collecting supplies. The sewing box can be made without sewing at all. You just use glue and starch the cloth to keep it in place. Jillian is excited. After reading the article, she selected a blue and grey piece of cloth 16” square to work with.

The measurements of the box are 7” \begin{align*}\times\end{align*} 6” \begin{align*}\times\end{align*} 4”.

Jillian decides to make a sketch of the box before beginning. Here is what her picture looks like.

The problem is that the box is not correct. It isn’t a box at all, it is a rectangle.

“You didn’t draw a three-dimensional picture,” her mother said, looking at her work.

**Jillian can’t remember how to do this. What do the dimensions mean? Which three-dimensional figure is a box? This Concept will help you figure all of these things out!!**

### Guidance

In Geometry so far, you have been learning about figures that are two-dimensional. Two-dimensional figures are ** plane figures** and we often think of them as “flat” figures. A plane figure does not have other dimensions of the figure shown. A plane figure is just that, it is a figure that is flat and does not have depth to it. Solid figures are known as

**, solids with flat surfaces that are polygons.**

*polyhedrons*Here are some plane figures:

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

**We can also have** *three-dimensional figures***. These are also known as** *solid figures***.** Solid figures aren’t created on one plane. They have depth to them. There are many different types of solid figures. **In this Concept, you will learn to classify solid figures.**

**Prisms**

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

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.

This is also a prism. It is a cube that takes the form of a number cube. We can find prisms everyday in real life.

Here we have a triangular prism. Notice that the two bases are triangles.

**Cylinders**

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.

Here is an example of a cylinder.

**A can of beans is a great example of a cylinder.**

**Pyramids**

A pyramid has one polygon as a base and the sides are triangular faces that all connect in one vertex at the top. We think of pyramids as Egyptian ones that have square bases, but any polygon can be the base of a pyramid.

This picture shows how the triangular faces of the pyramid reach one vertex at the top. You can’t really tell which polygon is the base in this picture. Let’s look at another one.

Here is a picture of a square pyramid. It has a square base, and the triangular faces reach one vertex at the top.

**Cone**

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

This is an example of a cone. You can see that the base of the cone is a circle.

**Sphere**

The final solid figure that you are going to learn about is a sphere. A sphere has a set of connected points located around one center point. While circular in form, it is also three dimensional. Here is an example of a sphere.

Don’t let this one fool you. You can see from the light that it is three dimensional in nature. This is an example of a sphere. Anytime you kick a ball, you are kicking a sphere!!

Identify the solid figures in the picture. Label each with its name and color.

#### Example A

What is the blue figure called?

**Solution: A cone**

#### Example B

What is the green figure called?

**Solution: A cube**

#### Example C

What is the red figure called?

**Solution: A pyramid**

Here is the original problem once again.

“My goodness Jillian, your quilting things are all over the place,” Jillian’s mother said to her one afternoon.

Jillian looked around the room. It was definitely true. Her supplies were everywhere.

“Maybe you should make a sewing box for yourself,” her mother suggested. “I have a pattern in a craft magazine that I have been reading and you can make it yourself.”

“That’s a great idea, thanks mom,” Jillian said, taking the magazine from her mother.

Jillian read the article on making the box and began collecting supplies. The sewing box can be made without sewing at all. You just use glue and starch the cloth to keep it in place. Jillian is excited. After reading the article, she selected a blue and grey piece of cloth \begin{align*}8\frac{1}{2}\end{align*}” square to work with.

The measurements of the box are 7” \begin{align*}\times\end{align*} 6” \begin{align*}\times\end{align*} 4”.

Jillian decides to make a sketch of the box before beginning. Here is what her picture looks like.

The problem is that the box is not correct. It isn’t a box at all, it is a rectangle.

“You didn’t draw a three-dimensional picture,” her mother said, looking at her work.

Jillian can’t remember how to do this. What do the dimensions mean? Which three-dimensional figure is a box?

**To work on this drawing, Jillian needs to draw a solid to show the length, width and height of the box that she is going to create. A box is a type of prism. Jillian’s box is going to be a rectangular prism. It will have two rectangular bases and then four sides to define it.**

**Here is a diagram of her rectangular prism.**

**Next we can compare this diagram with a picture of the sewing box.**

**You can see how the rectangular prism and sewing box are one in the same. Now Jillian can label the measurements of her box and begin to create it.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Plane Figure
- a flat two-dimensional figure.

- Solid Figure
- a three-dimensional figure with height, width and depth.

- Prism
- a solid with two parallel congruent bases.

- Cylinder
- a solid with two parallel congruent circular bases.

- Pyramid
- a polygon for a base and triangular faces that meet at one vertex.

- Cone
- a solid with a circular base and one vertex

- Sphere
- a three-dimensional circular solid

### Guided Practice

Here is one for you to try on your own.

Name the figure pictured here.

**Answer**

This figure has rectangular faces. It is a prism.

### Practice

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

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Directions: Name each type of prism.

11.

12.

13.

14.

15. What type of figure has a circular base and one vertex?

Cone

A cone is a solid three-dimensional figure with a circular base and one vertex.Cylinder

A cylinder is a solid figure with two parallel congruent circular bases.Plane Figure

A plane figure is a flat, two-dimensional figure.Prism

A prism is a three-dimensional object with two congruent parallel bases that are polygons.Pyramid

A pyramid is a three-dimensional object with a base that is a polygon and triangular faces that meet at one vertex.Solid Figure

A solid figure is a three-dimensional figure with height, width and depth.Sphere

A sphere is a round, three-dimensional solid. All points on the surface of a sphere are equidistant from the center of the sphere.### Image Attributions

Here you'll learn to classify solid figures.

## Concept Nodes:

Cone

A cone is a solid three-dimensional figure with a circular base and one vertex.Cylinder

A cylinder is a solid figure with two parallel congruent circular bases.Plane Figure

A plane figure is a flat, two-dimensional figure.Prism

A prism is a three-dimensional object with two congruent parallel bases that are polygons.Pyramid

A pyramid is a three-dimensional object with a base that is a polygon and triangular faces that meet at one vertex.Solid Figure

A solid figure is a three-dimensional figure with height, width and depth.Sphere

A sphere is a round, three-dimensional solid. All points on the surface of a sphere are equidistant from the center of the sphere.