Circle: Circumference

The distance around the outside of a circle is called the circumference (sometimes we think of it as the perimeter of a circle).

The formula for the circumference of a circle can be written in two ways: $d\pi$ or $2r\pi$

These forumulae are identical because $d$ stands for diameter and $r$ stands for radius -- and the radius (the distance from the center to the edge of a circle) is always half of a diameter (the distance, through the center, from edge to edge of a circle).  See the lesson Circles (Diameter vs. Radius) for more information.

So, to find the circumference of a circle, you multiple the diameter times pi.  If you are given the radius, instead of the diameter, multiply the radius times two to get the diameter, and multiply times pi.

Example:

Find the circumference of the following circle:

The diameter = 10 inches.

Circumference= $d\times \pi=10 \times \pi = 10 \pi$

Some assignments will let you stop at $10\pi$.  Other times you have to calculate the radius in inches.

Use $3.14$ or $\dfrac{22}{7}$ for pi.

 Circumference = $3.14 \times 10 = 31.4 \text{inches}$ Circumference = $\dfrac{22}{7} \times 10 = \dfrac{220}{7}=31.4 \text{inches}$

• Circle: Circumference

1. Find the circumference of a circle with a radius of 12 inches.

2. Find the circumference of a circle with a diameter of 8 inches.

3. Find the circumference of the circle:

4. Find the circumference of the circle:

5. If the circumference of a circle is 942 feet, what is the length of the diameter?

6. Find the circumference of a circular ampitheater if the length across its center is 450 feet.

7. If a circular room has a radius of 25 feet, what is the circumference of the room?

8. If a circular field has a diameter of 25 feet, what is the circumference of the field?

9. If the circumference of a swimming pool is 188.4 feet, how long is the radius of the swimming pool?

10. You want to wrap a ribbon around the bottom of a skirt that forms a circle when laid out flat on the ground.  If the measurement from the center of the circle to the edge of the skirt is 16 inches, how long a ribbon do you need?