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## 7th grade (Illustrative Mathematics)

### Unit 3: Lesson 5

Lesson 8: Relating area to circumference

# Area of a circle

The area of a circle is pi times the radius squared (A = π r²). Learn how to use this formula to find the area of a circle when given the diameter. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Where did the name pi originate from?
(19 votes)
• Although the constant that π represents has been known for thousands of years, it has been depicted by various symbols.

There is some uncertainty about who was first person to use π for this constant. The earliest confirmed usage was by William Jones in 1706. However, it is quite possible that John Machin might have been the first to use it a few years earlier than William Jones.
(2 votes)
• question:how many millimeters are in a meter? also, how many meters are in a kilometer?
(14 votes)
• There are 1,000 millimeters in a meter, and 1,000 meters in a kilometer. This tells us that there are 1,000,000 millimeters in a kilometer!

Have a blessed, wonderful day!
(3 votes)
• Find the area of a circle with a circumference of 12.56
How should I do this problem i have been stuck on it forever and the videos aren't helping
(9 votes)
• The circumference of a circle and the area of a circle have one thing in common: the radius.
If I were you I'd do it in two steps:
- first calculate the radius using the circumference formula,
- then calculate the area using the radius you just calculated :-)
Hope that helps!
(6 votes)
• How do i type the pi symbol on the keybord?
(7 votes)
• I usually use Alt key codes, such as, Alt + 227 = π. Try it, it's easy.
(8 votes)
• If you are already squaring the radius then why do you have squared in your final answer?
(1 vote)
• No, you do not that one time you square the radius will the only time you will square it.
(4 votes)
• What's the signficance of squaring mm? Is there a difference between mm and mm2?

Thanks.
(5 votes)
• The same difference as betweem m and m2: mm (and m) is a unit of length, and mm2 (and m2) is a unit of area
(3 votes)
• if you know the area how do to find the circumference, diameter and radius
(1 vote)
• Area = Pi*R^2

To find the radius (R), divide the area by Pi, then take the square root.

Once you have the radius (R), you can use it to find diameter and circumference.
Diameter = 2*R
Circumference = 2*Pi*R

Hope this helps.
(10 votes)
• how many number were discovered foe pie?
(3 votes)
• How could you remember all the digits of pi with out looking on a piece of paper
(2 votes)
• That is impossible. π has infinitely many digits. It is both irrational and transcendental. π never repeats and it never ends. To date, π has been computed to 10000000000050 digits.

At this level of study (and beyond) it is customary just to report your answer in terms of π. Thus, if you had an area that was 4.2π cm², then that is how you would normally report it. You would not typically report it as something like 13.19 cm².

If you do need an easily remembered estimate of π, the most useful one is 355/113 which is accurate to seven decimal places. That is 99.9999915% accurate, whereas 22/7 is only 99.95975% accurate.)
(5 votes)
• What if the radis, diameter, and circumerance was all decimals?
(1 vote)
• You can still solve for the area of a circle in the same way. You just would be multiplying decimals in the area equation instead of integers.
(6 votes)

## Video transcript

A candy machine creates small chocolate wafers in the shape of circular discs. The diameter of each wafer is 16 millimeters. What is the area of each candy? So the candy, they say it's the shape of circular discs. And they tell us that the diameter of each wafer is 16 millimeters. If I draw a line across the circle that goes through the center, the length of that line all the way across the circle through the center is 16 millimeters. So let me write that. So the diameter here is 16 millimeters. And they want us to figure out the area of the surface of this candy, or essentially, the area of this circle. And so when we think about area, we know that the area of a circle is equal to pi times the radius of the circle squared. And you say, well, they gave us the diameter. What is the radius? Well, you might remember the radius is 1/2 of the diameter. It's the distance from the center of the circle to the outside, to the boundary of the circle. So it would be this distance right over here, which is exactly 1/2 of the diameter, so it would be 8 millimeters. So where we see the radius, we could put 8 millimeters. So the area is going to be equal to pi times 8 millimeters squared, which would be 64 square millimeters. And typically, this is written with pi after the 64. So you might often see it as this is equal to 64 pi millimeters squared. Now this is the answer, 64 pi millimeters squared. But sometimes, it's not so satisfying to just leave it as pi. You might say, well, I want to get a estimate of what number this is close to. I want a decimal representation of this. And so, we could start to use approximate values of pi. So the most rough approximate value that tends to be used is saying that pi, a very rough approximation, is equal to 3.14. So in that case, we could say that this is going to be equal to 64 times 3.14 millimeters squared. And we can get our calculator to figure out what this will be in decimal form. So we have 64 times 3.14, gives us 200.96. So we could say that the area is approximately equal to 200.96 square millimeters. Now if we want to get a more accurate representation of this-- pi actually just keeps going on and on and on forever-- we could use the calculator's internal representation of pi, in which case, we'll say 64 times, and then we have to look for the pi in the calculator. It's up here in this yellow, so I'll do this little second function. Get the pi there. Every calculator will be a little different. But 64 times pi. And now we're going to use the calculator's internal approximation of pi, which is going to be more precise than what I had in the last one. And you get 201-- so let me put it over here so I can write it down-- so more precise is 201. And I'll round to the nearest hundreds, so you get 201.06. So more precise is 201.06 square millimeters. So this is closer to the actual answer, because a calculator's representation is more precise than this very rough approximation of what pi is.