Diameter and Circumference Related with Pi

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  • 0:03 Our Circle
  • 0:43 The Formula
  • 1:04 Pi
  • 1:45 Using the Formula
  • 3:46 Lesson Summary
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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.

Our 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.

The Formula

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.

Using the Formula

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?

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