how do you find the circumference of a circle with the radius

Formula for circumference

What exactly is the circumference of a circle? It'south actually defined as the length of the border surrounding a circumvolve, that is, the perimeter of a circle. We need to utilize $\pi$ to help us observe the circumference. The formula for finding the circumference includes the diameter, and looks like this:

C = $\pi$ d

To make this easier, we can also detect the circumference if we know the radius of a circumvolve. We know that the bore is equalled to 2r (2 times the radius), then in other words, the formula for a circle'south circumference is:

C = ii $\pi$ r

Either of these circumference formulas tin be used to assistance you solve problems.

How to find the circumference of a circle

We'll practice a 3 examples to help y'all learn how to discover the circumference of a circle using the formulas we just learned.

Question:

Find the circumference of the following circle:

Solution:

C = two $\pi$ r
C = 2 $\pi$ (7)

C = 43.98cm

In this case, we are given a circle, with only i of its characteristics given to united states. The 7cm is the measurement of the line from the center of the circumvolve to its border, which is, in other words, the radius of the circle. Luckily, we accept a circumference formula to help us out when we know the radius: C = 2 $\pi$ r. Simply by substituting in r with vii, nosotros're able to find that the circumference is 43.98cm.

Question:
Find the circumference of the following circle:

what is the circumference of the circle given the radius — What is the circumference of the circle given the radius

Solution:

C = 2 $\pi$ r
C = two $\pi$ (8½)

C = 53.41m

One time again in this example, we're given the radius of the circumvolve. Although information technology's non a make clean number like our previous example, but nosotros can nevertheless merely plug the number directly into the formula like what we did above. Exist aware of the units that this circumvolve's radius is given in and remember to give your last reply in the same unit of measurement. In this question, nosotros observe that the circumference is equalled to 53.41m.

Question:
Find the circumference of the following circle:

Solution:

C = $\pi$ d
C = $\pi$ (17)

C = 53.41m

In this example, we aren't given the radius. We're given the altitude across a circle through its center, which is as well called the diameter of a circumvolve. Again, referring dorsum to the 2 equations we can use to summate a circle'due south circumference, nosotros detect that i of them merely uses C = $\pi$ d. When we substitute "d" with 17, we find that we'll get the answer of 53.41m.

An interesting point to annotation is that you tin can however use the other formula for finding the circumference that uses the radius. All we take to do is first change the diameter into a radius. We know that the diameter is two times the radius, and so therefore, nosotros can divide 17 by 2 to notice the radius of 8.5 You can see that this number is actually the same one as the radius given in the previous circumvolve, and therefore, we get the same respond when nosotros utilise the C = 2 $\pi$ r formula.

More often than not, it's easier to use whichever formula corresponds with the characteristics of the circle you are given. Yet, if yous're unable to remember both of the formulas, you tin can always manipulate the info you're given so that information technology fits into the formula you do recollect.

Feel free to play effectually with this online circle figurer to see how the circumference changes as the bore and radius changes.

Source: https://www.studypug.com/geometry-help/circles-and-circumference

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