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## Basic geometry and measurement

### Course: Basic geometry and measurement > Unit 10

Lesson 1: Area and circumference of circles- Radius, diameter, circumference & π
- Labeling parts of a circle
- Radius, diameter, & circumference
- Radius and diameter
- Radius & diameter from circumference
- Relating circumference and area
- Circumference of a circle
- Area of a circle
- Area of a circle
- Circumference review
- Area of circles review

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# Radius & diameter from circumference

CCSS.Math:

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?(25 votes)
- The circumference given the radius can be found using C = 2πr

C is the circumference

r is the radius(9 votes)

- um i really need help with this i keep getting confused with circumference and radius(13 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!(24 votes)

- no it did not help what is 3.14(9 votes)
- 3.14 is π (pi, and infinite number) rounded to the nearest hundredth.(13 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.(4 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)

- A wet bicycle tire leaves a trace of water on the floor. The tire has a radius of 30, and the bicycle wheel makes 3 full rotations before stopping.

How long is the trace of water left on the floor?

Round your answer to the nearest

I don't get that(3 votes)- Each rotation produces a trace of water with length equal to the wheel’s circumference. Since the radius is 30, the circumference is 2pi*30 = 60pi.

So 3 rotations would produce a trace of water with length 3*60pi = 180pi.(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**!(3 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).(2 votes)

- If Radius is 3 = diameter 6

Diameter 10 = radius 5

Circumference of the Circle-

Radius = 2.

Formula -2pir

2 x 3.14 x 2=

Diameter =2

3.14 x 2= C(4 votes)- Except that you are only giving an approximation of the circumference. If R = 2, then C = 4π, and if D=2, C = 2π both are exact answers.(0 votes)

- Does anyone know the formula for the circumference of a circle.(1 vote)

## 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.