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Remedial Algebra I25 chapters | 248 lessons | 1 flashcard set

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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.

After watching this video, you will be able to tell others how the number pi is related to a circle's diameter and circumference. And using your newfound knowledge, you will be able to calculate the circumference or diameter of a circle.

We begin with a circle. After all, the number pi is pronounced the same way as a slice of pie from a big round yummy apple pie. In math, the number pi is approximated by 3.14 but the number actually goes on forever. We have to have a circle because both the circumference and diameter are parts of a circle.

The **circumference** is the distance around the circle, and the **diameter** is the distance across the circle going through the center. Think of the circumference as the amount of whipped cream you need to go all the way around the pie, and think of the diameter as the cut you make to cut the pie in half exactly.

In math, we have a formula that relates these two parts of a circle. This formula is called the **circumference formula**, and it is *C* = pi**d* where *C* stands for the circumference and *d* stands for the diameter. And pi is pi or 3.14.

This formula is actually quite interesting if you think about it. It relates the number pi to both the circumference and diameter. You can see that by dividing the circumference by the diameter, you will get the number pi. This is true for all circles! And for all circular pies! Isn't that cool?

You can view it as how the circumference and diameter of a circle are related to each other. Because of this relationship, we can calculate the circumference if we only know the diameter, and vice versa. Pi, as we know, is a mathematical constant and never changes. It will always be approximated by 3.14.

So, how do we use this formula? Let's take a look.

Say you are at a bakery, and the baker comes out with this beautiful, delicious chocolate mousse pie and tells you that the diameter of this particular pie is 10 inches. In conversation, he finds out that you are taking a math class, and he gets excited because he has a problem. So, he asks you if you can tell him the circumference of the pie because he needs to know how much whipped cream he needs so he can cover the whole outer edge of the pie. You tell him not to worry because you know exactly what you need to do.

You get out your handy little notebook, and you write down the formula *C* = pi**d*. You plug in 10 inches in for *d*, the diameter. Now all you need to solve for the circumference, *C*, is to multiply the diameter by pi. Doing this you get 3.14*10 = 31.4 inches. It takes you less than a minute to do all this, so you quickly answer the baker that he needs enough whipped cream to cover 31.4 inches to go all the way around the pie. The baker is delighted!

Now, let's change the scenario around a bit. Say the baker wanted to know the diameter of the pie instead of the circumference. Say the baker tells you that the circumference is 10 inches. How do you find the diameter?

You use the same formula, and you plug in 10 inches for *C*, the circumference. Doing this, you get 10 = 3.14**d*. To solve for *d*, you now need to divide both sides by pi or 3.14. Doing this, you get 10/3.14 = 3.18 inches, which tells you that the diameter is 3.18 inches. That is the distance across the pie or how long the cut is that will cut the pie exactly in half.

Now that you know the relationship between the circumference and diameter of a circle and you know how to calculate the circumference or diameter given the other, let's recap. We've learned that the **circumference** is the distance around the circle and the **diameter** is the distance across the circle going through the center. Both are parts of a circle.

The **circumference formula**, *C* = pi**d*, tells you how the circumference and diameter are related. To use this formula, you plug in the value that you are given and you use algebra to solve for the missing information. To find the circumference given the diameter, you multiply the diameter by pi. To find the diameter given the circumference, you divide the circumference by pi.

At the end of this lesson you should be able to:

- Note the correlation between the diameter and circumference of a circle
- Calculate the circumference or diameter of a circle using pi and the circumference formulas

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Remedial Algebra I25 chapters | 248 lessons | 1 flashcard set

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