Math Made Easy—How to Find the Circumference of a Circle
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:
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
#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 = πr2 and solving:
- 78.5 = πr2
- 78.5 = (3.14)r2
- 25 = r2(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.
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