10.5: Classifying Solid Figures
Introduction
The Sewing Box
“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 lesson will help you figure all of these things out!!
What You Will Learn
In this lesson you will learn the following skills:
- Classify solid figures as prisms, cylinders, pyramids, cones or spheres.
- Identify faces, edges and vertices of solid figures.
- Select real-world examples of given solid figures.
Teaching Time
I. Classify Solid Figures as Prisms, Cylinders, Pyramids, Cones or Spheres
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 polyhedrons, solids with flat surfaces that are polygons.
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 lesson, 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 an example 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.
1.
2.
3.
4.
Take a few minutes to check your work with a friend.
II. Identify Faces, Edges and Vertices of Solid Figures
In the last section you learned to identify different types of solid figures. We referred to the “sides of the figure” and to the “bases of the figure.” Well, there are different parts of each solid and knowing the names of these parts can help us with identifying them.
Three Parts of a Solid
- Faces
- Edges
- Vertices
These three parts are relevant to any solid that has flat surfaces, places where flat surfaces intersect and places where planes intersect.
Let’s define each part.
Face – any flat surface
The flat surface that makes the front of this cube is called a face. Many solid figures have more than one face.
Edge – The line segment where two faces meet. You can see by looking at this cube that the faces intersect in a line. That line is called an edge.
Many solid figures have more than one edge.
Vertex – a point where several planes meet in a point.
The arrow here is pointing to a vertex of this cube. Many solids have more than one vertex, we call those vertices.
Let’s look at identifying the number of faces, edges and vertices of different solids.
Here is a square pyramid.
I know this seems confusing. Think about it as if you were looking down on the pyramid. Now let’s look at the faces, edges and vertices.
The faces are the triangle sides and the square bottom. Given this, there are 5 faces in this pyramid.
The edges are where two flat surfaces meet in a line segment. Given this, there are 8 edges in this pyramid.
Faces come together at a vertex. There are five vertices in this pyramid.
Try this out. Identify the number of faces, edges and vertices of the following solid.
Take a few minutes to check your work with a partner.
III. Select Real-World Examples of Given Solid Figures
Throughout this lesson you have seen some real-world examples of different solids. Look around your classroom and see if you can find at least five different solids.
Here are a few more. See if you can identify each one.
This is a cylinder. Is that what you chose?
This is a sphere. Is that what you chose for an answer?
This is a rectangular prism. Is that what you chose?
Keep your eye out and you will find solid figures all around you!!
Real Life Example Completed
The Sewing Box
Here is the original problem once again. Reread it and underline any important information.
“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 that are found in this lesson.
- 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
- Face
- any flat surface on a solid figure
- Edge
- when two faces meet in a line segment. The line segment is the edge.
- Vertex
- when three or more faces meet at a single point.
- Polyhedron
- a solid figure with flat surfaces that are polygons.
Time to Practice
Directions: Look at each figure or picture and determine whether each is a prism, pyramid, cylinder, cone or sphere.
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Directions: Name each type of prism.
11.
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14.
Directions: Identify the part of each solid indicated by the arrow.
15.
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18. Define face.
19. Define edge.
20. Define vertex.
Directions: In this section, go on a scavenger hunt in your home or classroom and come up with two examples of each of the following solids.
21. Prism
22. Pyramid
23. Cone
24. Sphere
25. Cylinder
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