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### Course: Geometry (all content) > Unit 7

Lesson 8: Area and circumference of circles- Radius, diameter, circumference & π
- Labeling parts of a circle
- Radius and diameter
- Radius, diameter, & circumference
- Circumference review
- Radius & diameter from circumference
- Circumference of a circle
- Area of a circle
- Area of a circle
- Area of circles review
- Area of parts of circles
- Area of a circle intuition

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# Radius & diameter from circumference

Sal finds the radius and diameter of a circle given the circumference.

## Want to join the conversation?

- I need help, How do u find the circumference with the given radius?(41 votes)
- The circumference given the radius can be found using C = 2πr

C is the circumference

r is the radius(19 votes)

- um i really need help with this i keep getting confused with circumference and radius(19 votes)
- The circumference is the distance around the circle. In other words, the circle's perimeter.

The diameter is a straight line that passes through the center of the circle.

The radius is half of the diameter. It starts from a point on the circle, and ends at the center of the circle.

Hope this helps!(34 votes)

- who else is studying in their summer break cause i am

asian parents(21 votes)- fr bro im in 3rd grade and this topic kind of hard but can get this!(3 votes)

- no it did not help what is 3.14(6 votes)
- 3.14 is π (pi, and infinite number) rounded to the nearest hundredth.(17 votes)

- do you guys have a step by step for the area of the circle because i am not understanding because i am in 7th grade and i need to know more(6 votes)
- Imagine you have a round pizza. The area of a circle is like the amount of space inside that pizza. It tells you how much surface area the circle covers.

To find the area of a circle, we use a special number called pi, which is approximately 3.14. Pi helps us figure out how much space is inside the circle.

The formula to find the area of a circle is: Area = pi times the radius squared.

The radius is a line that starts at the center of the circle and goes to the edge. If you cut the circle in half, the radius would be the distance from the center to the edge.

To find the area, we need to know the radius. Once we have the radius, we square it by multiplying it by itself. Then, we multiply that squared radius by pi.

For example, let's say the radius of a circle is 5 units. We square the radius: 5 x 5 = 25. Then, we multiply the squared radius by pi: 25 x 3.14 = 78.5.

So, the area of the circle with a radius of 5 units is 78.5 square units. It means that if you measured the inside of that circle, it would cover an area of 78.5 square units.

Remember, the area is a measure of space inside the circle, like the space on a pizza. And we find it using the formula: Area = pi times the radius squared. please upvote if this helps(15 votes)

- this is super confusing :|(10 votes)
- okay so if to find circumference= 2pir could it just be diameter x pi? To find circumference?(7 votes)
- Yes, both ways work. The only reason to use one or the other is if you are only given the number of the radius or if you are only given the number of the diameter.(5 votes)

- so the diameter x Pi = my answer? i feel a tad bit lost.(5 votes)
- yes C=πd or C=2πr which is radius times 2 times pi(6 votes)

- So circumference and diameter are always the same numbers?(4 votes)
**The circumference is the diameter times pi**(𝝅).**Example**:**If the diameter is 12 then the circumference is 12**𝝅

𝝅**is generally difficult to calculate, since it goes on forever you can write it in terms of**𝝅 (**12**𝝅).**You could also times the diameter by 3.14 to estimate it**.**Example**:**If the diameter is 12 then the circumference is 37.68**.**Hope This Helps**!(5 votes)

- SO how do i find the radius by just knowing the circumference? Why did he divide 49 by 2 pi? where did 2 come from?(3 votes)
- If you start from the circumference formula, C=2πr, to isolate the r, you have to divide by 2π, thus r= C/(2π).(3 votes)

## Video transcript

- [Voiceover] Let's say that
we know that the circumference of a circle is 49 pi. Based on that, let's
see if we can figure out what the radius of that
same circle is going to be. And I encourage you, and I'll write equals here. And I encourage you to pause the video, and see if you can figure
it out on your own. Let's just draw the circle
to help visualize it. I'll just do a hand-drawn circle, clearly not a perfect
circle right over here. We know that if its radius is of length r, that the circumference is going to be two pi times r. So, I could write the circumference is equal to two pi times r. In fact, the number pi, the standard definition for it, is just the ratio between the
circumference and the diameter of a circle. Now, why is that? Well, if the diameter here is two r, right? We have r and then have another r. We see that the circumference
is pi times two r, or we can say that the ratio
between the circumference and the diameter, which is the ratio between c and two r, that's just going to be pi. Anyway, I've gone on longer than I need to just to solve this problem. We can go to this original formula here, saying the circumference
is two pi times r, and we can just substitute in
49 pi for the circumference. So, we could say 49 pi is going to be equal to
two pi times the radius. Now, let's see, we can
divide both sides by two pi to solve for r. So, dividing both sides by two pi. On the right-hand side,
the two pis cancel out. On the left-hand side, pi
divided by pi cancels out. 49 divided by two is 24.5. So, if the circumference
is 49 pi whatever units, then the radius is going to be 24.5 of those units. Let's do one more of these. Let's say that we have a circle whose circumference, I'll just say C, is equal to 1600 pi. My question is what is the diameter? The diameter of the
circle is equal to what? Just as we said that the circumference could be written as two pi r or as pi times two r, two r is just the diameter. So, we could say that the
circumference is equal to pi times the diameter. Once again, that comes out of
that traditional definition of pi as the ratio
between the circumference and the diameter. You could say that the ratio
between the circumference and the diameter is equal to pi. Circles are this very fundamental
thing in the universe, and you take the ratio of the circumference and the diameter, you get this magical and
mystical number that we see that keeps popping up in mathematics. Anyway, back to the problem. If we say the circumference is 1600 pi, and this is equal to
pi times the diameter, we can just divide both sides by pi to get the diameter, which is going to be 1600. The circumference is 1600 pi units, whatever units those are, maybe meters. Then, the diameter is
just going to be 1600 of those units, or in
this case, maybe meters. And we're all done.