If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: 7th grade (Eureka Math/EngageNY)>Unit 6

Lesson 4: Topic D: Problems involving area and surface area

# Finding circumference of a circle when given the area

Learn how to find the circumference, the distance around a circle, when given the area. Created by Sal Khan.

## Want to join the conversation?

• why the formula of the area of the circle is taken a pi*r^2?
• so you multiply pi by the radius squared to get circumference, please tell me if im wrong.
• no what you are telling is the formula for area of a circle. the formula for circumference of a circle is 2 x pi x r(radius).
Hope your confusion is clear now.
• Is it possible to calculate the perimeter of a sphere?
We had done perimeter of a rectangular prism in class, but wanted to find out for sphere. Thanks to anyone who answers.
• Well you could find the diameter, radius, and surface area of a sphere, but that usually comes later.

Here is the formula if you're curious...

A = 4 π r^2

Hope this helps!
• how did he go from radius squared=36 to radius=6 in the video ? He said something about the principles or whatever so does that apply for any/every problem like this?
• So opposite of squaring is square root, x= ±√36, when we take the square root we can get a positive or negative answer x=6 or x=-6. However, in many practical problems (such as finding the radius), we know we cannot have a negative distance for radius, so we only pick the positive (6)
• How would you find the area of a circle when given the circumference? I am struggling on this one problem. It states:
"A sumo wrestling ring is circular and has a circumference of 4.6pi meters."

"What is the area A of the sumo wrestling ring in square meters?"
• it is 4.6 divided by two to get the radius of 2.3, and then you square it to get 5.29 pi, which is le answer :)
• his voice sounds like my old math teacher
• thy mortal should not adress thine sacred teacher in such a direspectful way. Gandalf has been offended. Thy mortal has commited a serious offense
• I'm looking for "How to figure out the circumference of a Circle" by knowing the diameter. I can't figure out how, such and such to figure out the circumference by knowing the diameter.
• If you know the diameter, then you would multiply the diameter by pi. Pi is 3.14, so if the diameter was 3, then the circumference would be 9.42. I would appreciate an upvote, as I'm trying to get a badge. :)))
• Can you solve this question with π=23/7
• Yes. All you have to do is divide 23 by 7 and you have your answer (pi=3.28571428571, which is not correct because the simplification of pi is 3.14)
• At , what do you mean by "pie"?I 'm not getting this.
• How come I get REALLY CONFUSED when watching these videos? And, I can't understand anything y'all be talking bout.
• yeah, i get confused and have to watch them twice. but i just try and find the formula and write it down that way i can aply it to my work

## Video transcript

If we know some circle has an area of 36pi-- so it has an area of 36pi-- can we figure out what the circumference of this circle is? And I encourage you to pause this video, and try to think about that question. Well, from the area, we could figure out what the radius is, and then from that radius, we can figure out what its circumference is. So we know that the area, which is 36pi, is equal to pi r squared. And so if you look at it on both sides of this equation, if we divide-- let me rewrite it so it's a little bit clearer in a different color. So we could set up an equation pi r squared is equal to 36pi. Now, if we want to solve for the radius the first thing that we might want to do is divide both sides by pi. Then, we're left with r squared is equal to 36. Now, if we just solve this as a pure math equation, you might say, OK, we could take the positive and negative square root of 36. r could be plus or minus 6, but we need to remember that r is a distance, so we only care about the positive. So if we take the principal root of 36, we get r is equal to 6. From there, we can use this to figure out the circumference. So the circumference is equal to 2 pi r. Circumference is equal to 2 pi r. And in this case, r is equal to 6. So it's equal to 2 pi times 6, which is going to be equal to 12pi. So that's straightforward, area 36pi, we leverage pi r squared to figure out that the radius was 6, and then from that we were able to figure out that the circumference was 12pi.