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Algebra II: High School23 chapters | 203 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson, and you will learn what makes a circle a conic section. Also learn how to calculate the circumference of a circle. You will learn about the one important measurement that you need for any circle.

What is a circle? Why are they important? A **circle** is a round shape whose points are all the same distance away from a center point. This kind of shape is important because we use them in our everyday lives. Think about the way we travel. It would be rather difficult if we didn't have circles (our wheels) to take us from point A to point B. Just a quick look around you and you are bound to see circles in so many different applications. You see them in cars, bicycles and even our clocks. You can't escape them!

What makes circles even more interesting in math is that they are also considered a **conic section**. What does this mean? This means that a circle is a shape that you get by cutting a cone. Picture an ice cream waffle cone. Now picture a knife slicing straight across. What kind of shape do you end up with? Why, a circle!

Notice how perfectly round it is:

Just like your cone has a center, our circle also has a center. When you cut a cone to get a circle, our circle's center is the same center as our cone.

The center is a very important point for our circle. It comes into play when we need to calculate the distance of our circle. In math, we call this distance around our circle, the **circumference**, and of course, we would have a formula for this. This formula is *C* = *pi* * *d*, where *C* stands for the circumference, *pi* for the mathematical constant that is approximated by 3.14, and *d* stands for the diameter of the circle. The **diameter** of our circle is the distance it takes to walk from one edge of the circle clear across the circle to the other edge, making sure that you are walking through the center of the circle. You can also calculate the diameter of the circle as twice the distance from the center of the circle to the edge.

Now, let's see how we can use our distance formula, our circumference formula, to find the circumference of a circle if we know the circle's diameter. Let's say we are given a circle and are told the circle's diameter is ten inches. We need to find the circumference of this circle. How do we do this? Well, we remember our formula for the circumference of a circle, *C* = *pi* * *d*. We see that all we need to do is to plug in our value for the diameter, and then multiply it by *pi* to find our answer. So, let's see what our answer is. *C* = 3.14 * 10 which is equal to 31.4 inches. There we have it. Our answer is 31.4 inches, and we are done!

Let's review what we've learned. We've learned that a **circle** is a round shape where all the points are the same distance away from a center point. It's a **conic section** because it is a shape you can get by cutting a cone. The **diameter** of a circle, the distance from one edge of a circle to the opposite side going through the center, is a circle's most important measurement. It is this measurement that we need to calculate our **circumference**, the distance around the circle. The formula for circumference is *C* = *pi* * *d*, where *C* stands for the circumference, *pi* for the mathematical constant that is approximated by 3.14 and *d* stands for the diameter of the circle. To use it, we simply need our diameter to plug in and then to multiply by *pi*.

This video lesson was developed to help you to:

- Define terms such as circle, diameter and circumference
- Explain why a circle is a conic section
- Use the distance formula to calculate the circumference of a circle
- Work through a sample problem involving the distance formula

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Algebra II: High School23 chapters | 203 lessons

- Defining and Graphing Ellipses in Algebra 5:00
- How to Write the Equation of an Ellipse in Standard Form 6:18
- The Circle: Definition, Conic Sections & Distance Formula 3:43
- How to Write the Equation of a Hyperbola in Standard Form 8:14
- The Parabola: Definition & Graphing 8:33
- How to Write the Equation of a Parabola in Standard Form 8:17
- How to Identify a Conic Section by Its Formulas 6:33
- Go to Algebra II: Conic Sections

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