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High School Trigonometry: Homework Help Resource30 chapters | 203 lessons

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Lesson Transcript

Instructor:
*Laura Pennington*

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

Solid figures are everywhere around us. In this lesson, we'll learn what solid figures are, and we'll explore some common types of solid figures. After going through the lesson, you will be able to test your new-found knowledge with a quiz.

**Solid figures** are three-dimensional objects. What this means is that solid figures have a width, a depth, and a height. For example, look at your computer, laptop, phone, or whatever else you are using to view this lesson. Notice that it has a width, a depth, and a height.

This may make you think that solid figures are probably quite common in the environment around us, and you are right! Anything with those three dimensions (width, depth, and height) is a solid figure, and because we live in a three-dimensional world, these figures are all around us. In mathematics, there are many solid figures.

Let's look at these figures and some examples of them in our everyday life.

A **rectangular prism** is a solid figure that has six sides, called faces, that are rectangles. This can be thought of as a fancy name for something that has the shape of a cardboard box. Rectangular prisms show up all around us. Some examples may include a book, a piece of furniture, or a jewelry box.

**Cubes** are just a special case of rectangular prisms. Cubes are solid figures that have six faces that are all squares of the same size. Since a square is a rectangle, a cube has six faces that are all rectangles, so a cube is a rectangular prism.

A **cone** is a solid figure that has a circular face on one end, called the base, and a point at the other end where the sides meet. I'm pretty sure we have all enjoyed an ice cream cone at one point in our lives. The cone that you put the ice cream in is an example of a cone, and what a delicious example! Some other examples could include a megaphone, a tee-pee tent, or a birthday party hat. We see that a parking cone is another example of a cone.

A **pyramid** is a solid figure that has a polygon as its base on one end and triangular faces all meeting at a single point on the other end. Many of us have heard of the Great Pyramids of Egypt. These are a perfect example of a pyramid in the world around us. Some other examples of pyramids in the world around us are rooftops, certain buildings, and figurines.

A **sphere** is a solid figure that is round and has the shape of a ball. For example, a basketball is a sphere. Another example of a sphere is the earth we are standing on! When we look at a globe, we see that the earth is three-dimensional and has the shape of a ball. Therefore, the earth is a sphere.

A **cylinder** is a solid figure that has two circular bases and one curved side. Remember when I explained what a cone is? Well, a cylinder is similar to a cone, except that rather than only one circular base and a point on the other end, there are circular bases on both ends connected by the curved side. Some examples of cylinders are tubes, tree stumps, poles, and cans.

Let's identify each of the following solid figures as rectangular prisms, cubes, spheres, pyramids, cylinders, or cones.

Identify the solid figure:

1.) This is a picture of a baseball. The baseball is a round solid figure that looks like a ball (because it is one!). Therefore, the baseball is a sphere.

2.) The second picture is a picture of a leather box. The leather box is a solid figure that has six faces that are all rectangles. Therefore, the leather box is a rectangular prism.

3.) The tin can in this picture is a solid figure that has two circular bases and one curved side. Therefore, the tin can is a cylinder.

4.) This beautiful blue spruce pine tree is a solid figure that has a large circular base as its bottom and a point at the top that all its sides meet at. Therefore, the tree is a cone.

**Solid figures** are simply three-dimensional objects, and we see them in our everyday life all the time. We've gone over some common solid figures and their properties. They are:

**Rectangular prism**- a solid figure that has six sides, called faces, that are rectangles**Cube**- a solid figure that has six faces that are all squares of the same size**Cone**- a solid figure that has a circular face on one end, called the base, and a point at the other end where the sides meet**Pyramid**- a solid figure that has a polygon as its base on one end and triangular faces all meeting at a single point on the other end**Sphere**- a solid figure that is shaped like a ball**Cylinder**- a solid figure that has two circular bases and one curved side

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High School Trigonometry: Homework Help Resource30 chapters | 203 lessons

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