## Formula for the circumference of a circle

Remember that the radius of a circle is the length from its center to a allude on its circumference,

and that the diameter is a special chord that passes through the facility of the circle. The diameter is constantly made of 2 radii, such that ???d=2r???.

You are watching: How to find the circumference of a quarter circle

And ???pi??? is a unique number, ???pi approx 3.14???, that describes the partnership between a circle’s circumference and also the size of its diameter.

**Circumference of a circle**

The circumference of a circle is the distance approximately the circle (its perimeter) and also it’s equal to ???2???, multiplied by ???pi??? and the radius, or simply ???pi??? times the diameter.

See more: Number Of Ridges On A Quarter S And Half, Why Do Quarters Have Ridges On Their Edges

???C=2pi r???

???C=pi d???

## Finding circumference given the diameter of the circle

**Example**

What is the circumference of a circle with a diameter of ???10 ext in????

The formula for the circumference of a circle when we know a circle’s diameter is ???C=pi d???. We understand the diameter of the circle is ???10 ext in??? so when we plug this in to the formula we get

???C=pi cdot 10???

???C=10pi ext in???

???Capprox 10(3.14) ext in???

???Capprox 31.4 ext in???

## Finding the circumference of a quarter circle

**Example**

To the nearemainder hundredth, what is the circumference of the arc of this quarter circle?

The formula for circumference once you understand the radius is ???C=2pi r???, and we recognize the radius is ???7??? feet, so the circumference is

???C=2pi (7) ext ft???

???C=14pi ext ft???

This is the full circumference, so we should divide this circumference by ???4??? to find the size of the arc.

???fracC4=frac14pi ext ft4=3.5pi ext ft???

Notice if we had actually been asked to uncover the perimeter of the number, we would have actually essential to include the lengths of the radii to this percent of the circumference. The perimeter would be

???Papprox 10.99 ext ft + 7 ext ft+7 ext ft???

???Papprox 24.99 ext ft???

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