Geometry

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# Perimeter of a Circle

## How to Find the Perimeter of a Circle

The perimeter of a circle is called the circumference. The formula for perimeter of a circle is the circumference formula. It is given as:**C = 2πr**

or:**C = πd**

Where *C* is the circumference, *r* is the radius of the circle, and *d* is the diameter of the circle. Here is an example of using this formula to find circumference of a circle with a radius of 3.

C = 2π(3) = 6π, circumference = 6π.

A circle with labeled dimensions.

### Example Problems:

**Problem 1:**

Find the circumference of a circle with a radius of 10.

Solution:

Let’s plug the radius into the circumference formula.

C = 2πr = 2π(10) = 20π**The circumference is 20π.**

**Problem 2:**

Find the circumference of a circle with a diameter of 10.

Solution:

Let’s plug the diameter into the circumference formula.

C = πd = π(10) = 10π**The perimeter is 10π.**

**Problem 3:**

Compare the perimeter of a circle with a diameter of 7 to a square with a side length of 7. The formula for perimeter of a square is P = 4s.

Solution:

Let’s plug the circle’s diameter into the circumference formula. Solving for circumference gives us the perimeter.

C = πd = π(7) = 7π.

Now let’s do the same for the square.

C = 4s = 4(7) = 28**The circle’s perimeter is 7π (≈22) and the square’s perimeter is 28.**