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# Calculating the Circumference of a Circle

[youtube id="6dyYbo0ebWo" width="600" height="340" position="left"]The circumference of a circle is the distance around the circle. It is useful to know if you need to wrap a circular object with some material.

The needed formulas are

*C=2πr*and

*C=πd.*

*C*stands for the circumference,

*r*stands for radius, and

*d*stands for diameter.

Why do we have two different formulas? Well, sometimes you will know the radius of the circle and sometimes you will know the diameter. Each formula can be derived from the other because we know that

*2r*is the length of the diameter because there is two radii in one diameter.

**Method 1:**

I am given that the diameter of a circle is 5 inches across.

Step 1. Plug in the needed information. In our example, we are going to use the formula

*C=πd*because we are given the diameter.

*C=πd * changes into* C=π(5)* once we have plugged in our given information.

*C=π(5)* is more accurately written as *C=5π*.

Step 2. Our final answer is 15π inches. To approximate, you can multiply 5 by 3.14 which is 15.7 inches. Please realize that 15π* *inches is more accurate, but 15.7 inches is acceptable in cases where the problem does not state “leave your answer in terms of π.

**Method 2:**

I am given that the radius of a circle is 3 cm.

Step 1.) Plug in the needed information. In our example, we are going to use the formula *C=2πr* because we are given the radius.

*C=2πr *changes into* C=2π(3)* once we have plugged in our given information.

* C=2π(3)* is rewritten as

*C=6π*.

Step 2.) Our final answer is 6π

*cm. To approximate, you can multiply 6 by 3.14 which is 18.84 inches.*