## Geometry Help

## Circumference of Circle

Understanding what the circumference of a circle is, as well as how to calculate the circumference of a circle is a relatively easy geometry principle. By following the circumference problems and solutions in the **Geometry Help Online** section below, you should easily be able grasp the concept of circumference.

By following along with the examples given and taking the online * Math Made Easy!* geometry quiz for circumference of a circle, you will be able to complete your geometry homework on this topic in a snap.

## Circumference of Circle Formula

The circumference of a circle is merely the distance around a circle. Sometimes it is referred to as the perimeter, although the term *perimeter* is usually reserved for the measure of a distance around a polygon.

**The equation for the circumference of a circle can be written in two ways:**

- C = 2πr
- C = πd

Where: r represents the radius of the circle and d represents a circle's diameter.

Recall that the radius is the distance from the center of the circle to a point on the edge of a circle and the diameter is the largest distance across a circle. The diameter is always twice the length of the radius.

When calculating the circumference with a known radius use the first version of the circumference formula shown; when the diameter is known use the second version of the circumference formula shown.

## Modern Day Uses for Circumference

Did you know that the circumference of the Earth was first calculated more than 2200 years ago by the Greek mathematician, Eratosthenes?

**Knowing how to calculate circumference is used in many fields of study, including:**

- engineers
- architects
- carpenters
- artists

## High School Geometry Help - Terms

**Circle Terms to Know:**

**Pi**: symbol for pi is π and it equals about 3.14**Radius**: The distance from the center of a circle to an edge**Radii**: The plural for radius.**Diameter**: The distance from one edge of a circle to another edge going through the center.**Circumference**: The distance around a circle; the perimeter of a circle.

## Math Made Easy! Tip

If you have trouble remembering geometry terms, it helps to think of other words from the same root with which you may be more familiar.

For example, the Latin root of the word circumference is *circum, *meaning* around*. *Circum* is now considered a prefix also meaning *around* or *round about*.

**Here is a list of words that come from the root/prefix circum that can help you remember that circumference the distance of measure around a circle:**

- Circus - (from the root
*circum*) usually held in a*circular*arena - Circle - (from the root
*circum*) a*round*shape - Circumvent - to go
*around*or bypass; to avoid - Circumstances - conditions
*surrounding*and event - Circumnavigate - to fly or sail
*around*

## Geometry Help Online: Circumference

Check out 4 common types of geometry homework problems and solutions involving the circumference of circles.

## Math Made Easy! Quiz - Circumference

For each question, choose the best answer. The answer key is below.

**What is the circumference of a circle with a radius of 1 cm.?**- 2 cm.
- 6.28 cm.
- 3.14 cm.

**What is the circumference of a circle with a diameter of 7 ft.?**- 21.98 ft.
- 43.96 ft.
- 14 ft.

**Find the circumference of a circle with an area of 153.86 cm. squared.**- 7 cm.
- 43.96 cm.
- 49 cm.

### Answer Key

- 6.28 cm.
- 21.98 ft.
- 43.96 cm.

## #1 Find the Circumference of a Circle Given the Radius

**Problem:** Find the circumference of a circle with a radius of 20 cm.

**Solution:** Plug in 20 for r in the formula C = 2 πr and solve.

- C = (2)(π)(20)
- C = 40π
- C = 125.6

**Answer:** A circle with a diameter of 20 cm. has a circumference of 125.6 cm.

## #2 Find the Circumference of a Circle Given the Diameter

**Problem: **Find the circumference of a circle with a diameter of 36 in.

**Solution: **Simply plug in 36 for d in the formula C = πd and solve.

- C = (π)(36)
- C = (3.14)(36)
- C = 113

**Answer: **The circumference of a circle with a diameter of 36 in. is 113 in.

## #3 Find the Radius of a Circle Given the Circumference

**Problem: **What is the radius of a circle with a circumference of 132 ft.?

**Solution: **Since we are trying to determine the radius, plug in the known circumference, 132, for C in the formula C = 2πr and solve.

- 132 = 2πr
- 66 = πr
*(divide both sides by 2)* - 66 = (3.14)r
- r = 21
*(divide both sides by 3.14)*

**Answer: **A circle with a circumference of 132 ft. has a radius of about 21 ft.

## #4 Find the Circumference of a Circle Given the Area

**Problem:** Find the circumference of a circle that has an area of 78.5 m. squared.

**Solution: **This is a two-step problem. First, since we know the area of the circle we can figure out the radius of the circle by plugging in 78.5 for A in the area of a circle formula A = πr^{2} and solving:

- 78.5 = πr
^{2} - 78.5 = (3.14)r
^{2} - 25 = r
^{2}*(divide both sides by 3.14)* - r = 5
*(take the square root of both sides)*

Now that we know the radius is equal to 5 m. we can substitute 5 in for r in the formula C = 2πr and solve:

- C = 2π(5)
- C = (2)(3.14)(5)
- C = 31.4

**Answer: **A circle with an area of 78.5 m. squared has a circumference of 31.4 m.

## Do you need more geometry help online?

If you still need help with other **geometry problems about the circumference of a circle**, please ask in the comment section below. I'll be glad to help out and may even include circumference math problem in the problem/solution section above.

## Comments

**unknown** on March 13, 2018:

thank you so much this article was so helpful i very much thank you!

**Kristin Trapp (author)** from Illinois on March 06, 2012:

I'm glad to help SmartAndFun.

**SmartAndFun** from Texas on March 06, 2012:

LOL, my daughter (the smarter one) figured that out. I am following you so that I'll be sure to be able to find you again. Dd is doing fairly OK in geometry this semester, but last semester (algebra) most of her homework sessions ended in tears. She got a 45 on an algebra assignment that she, my husband and I all worked on together for three hours. LOL, we thought between the three of us she'd get at least a C. We will need you again for sure! Thank you!

**Kristin Trapp (author)** from Illinois on March 06, 2012:

You are very welcome SmartandFun. Although looking back over my answer, somehow my pi symbol was replaced with a question mark. I am glad you could follow along.

**SmartAndFun** from Texas on March 06, 2012:

Thank you so much, KTrapp, you are a life saver! I was able to go over your answer with my daughter this morning before school, and we both get it now! She and I are both "arts and letters" type people and have a hard time with math. I feel terrible when she asks me for help. I try to help but truthfully she is ahead of me in the math dept. I see those symbols and letters (like the m) and my brain just freezes up. Thanks so much for helping us both! You are wonderful!

**Kristin Trapp (author)** from Illinois on March 06, 2012:

Smartandfun - Thanks for your question. I think I can help both you and your daughter. First, let's talk about Area. The Area of anything (circle, square, triangle, etc.) is always in terms of units squared. For example, a square where each side is 2inches has a perimeter (distance around) of 8inches and an area of 4inches squared. It's squared because we multiplied 2inches X 2 inches which = 4inches squared.

In example #4 the "m" simply represents the units (i.e. meters). It is "m squared" since the 78.5 represents the Area of the circle, and Area is always units squared.

I don't know the type of measurement (units) for your daughter's specific math problem, but whatever it is,those units would also squared.

But let's not get hung up on the units. What we know is that the Area of the circle is 200.96 and we want to figure out the circumference. If you look at the equations for the Area of a circle and the Circumference of a circle, they both have r (radius) in them. So if we could figure out the radius of the circle knowing the Area, then we could plug the radius of the circle into the Circumference equation in order to find the circumference.

So let's do that. We will let ?=3.14 to solve the problem:

step 1: A=2(?)r ^squared

step 2: 200.96 = ?r ^squared

step 3: 64=r ^squared (divide both sides of equation by 3.14)

step 4: 8=r (take the square root of both sides of the equation)

Now that we know the radius of the circle is 8 units we can substitute 8 for r into the circumference equation as follows:

C=2?r

C= 2?8 (we know r = 8 so plug it into the equation)

C=16? (multiple 2 X 8 to get 16)

C=16(3.14) (let ? = 3.14 to solve)

C=50.24units

Therefore, a circle with an Area of 200.96 units^squared has a radius of 8 units and a Circumference of 50.24 units.

I hope this helps. Thanks for asking.

**SmartAndFun** from Texas on March 05, 2012:

I am trying to help my 7th grade daughter learn how to figure the circumference of a circle when all that is known is the area, but I'm the blind leading the blind, LOL. I'm looking at the last example, and I am not understanding at all. The example you give has an area of 78.5 m squared. What do we do if the area in her question is not m or squared? What does the m stand for? The area in her question is 200.96. How does that plug into the formula? I do not get it at all! Thank you!

**shan** on February 15, 2012:

I GET IT

**Kristin Trapp (author)** from Illinois on January 23, 2012:

Fizzywoz - If you look at examples #1-#4 at the end of the article you can see how numbers are plugged into the equation. You will usually just plug in a known radius into the equation to figure out the circumference or you may plug in a known circumference to determine the radius. Let me know if you have any other questions. I appreciate your feedback.

**Fizzywoz** on January 23, 2012:

You havn't really explained what you do in the equations if you could just do that this article would be even more helpful :)

**Kristin Trapp (author)** from Illinois on October 24, 2011:

When my kids would tell me they weren't going to need the math that was being forced upon them, I always told them they were right. They probably never were going to need that exact math, but the value for most kids is in the exercise it gives their brains. Most colleges like to see 3-4 years of high school math so most kids have no choice but to find their way through it. No skating allowed anymore. The times they are a-changin'.

**Arlene V. Poma** on October 23, 2011:

k, k, k! I didn't need this stuff! I skated. But in California, you have to pass English and math to graduate. Ewwwwww. I would have flunked the math for sure!

**Kristin Trapp (author)** from Illinois on October 23, 2011:

I'm glad you remember Arlene, afterall you never know when you might need to figure out the circumference of something when you only know its radius. I think this is what makes frustrated math students ask, "when am I ever going to need this?"

**Arlene V. Poma** on October 23, 2011:

I am pulling my hair out, but I do remember how to do this.

**Kristin Trapp (author)** from Illinois on October 23, 2011:

Thank you Stephanie. A good attitude, as you put it, definitely helps when learning math. I think sometimes the pace in high school is too fast for some kids, especially when it is their first time ever learning some of these concepts.

**Stephanie Das** from Miami, US on October 23, 2011:

Of all math forms, geometry is the one that I have found most useful in my everyday life. These are little skills that we need to be reminded of from time to time. It also helps that I understand the importance of math and have a better attitude towards it now than I did when I was in high school! Voted up and useful.