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### Course: 7th grade > Unit 9

Lesson 2: Area and circumference challenge problems# 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?(6 votes)
- I was wondering about this as well but luckily for us Sal made a video that gives an intuition about this formula:

https://www.khanacademy.org/math/geometry/hs-geo-foundations/hs-geo-area/v/informal-argument-for-the-area-of-circle-formula(12 votes)

- so you multiply pi by the radius squared to get circumference, please tell me if im wrong.(7 votes)
- 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.(8 votes)

- 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.(8 votes)- 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!(3 votes)

- 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?

please answer back!(5 votes)- 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)(5 votes)

- At0:09, what do you mean by "pie"?I 'm not getting this.(4 votes)
- He's talking about the number pi, which is approximately 3.141593. This video introduces pi: https://www.khanacademy.org/math/geometry/cc-geometry-circles/circle-basics/v/circles-radius-diameter-and-circumference(3 votes)

- 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?"

"Give your answer in terms of pi."(5 votes) - his voice sounds like my old math teacher(5 votes)
- Can you solve this question with π=23/7(3 votes)
- 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)(2 votes)

- 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.(3 votes)
- 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. :)))(2 votes)

- How come I get REALLY CONFUSED when watching these videos? And, I can't understand anything y'all be talking bout.(2 votes)
- 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(3 votes)

## 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.