Circumference is the distance around a circle. We can find the circumference using either the diameter or radius of a circle.
For shapes made of straight lines, we say they have a perimeter. For circles, the perimeter gets the name circumference.
It does not matter if the circle is a slice of a sphere (like earth's equator) or flat like King Arthur's gathering place for all his knights if we know either the diameter or the radius, we can find the circumference of a circle. I bet King Arthur would have welcomed Sir Cumference to his Round Table.
A circle (the set of all points equidistant from a given point) has many parts, but this lesson will focus on three:
Two formulas are used to find circumference, , depending on the given information. Both circumference formulas use the irrational number Pi, which is symbolized with the Greek letter, . Pi is a mathematical constant and it is also the ratio of the circumference of a circle to the diameter.
If you are given the circle's diameter, , then use this circumference of a circle formula:
If you are given the radius, r, you can still find the circumference. If you know the radius, the circumference formula is:
You can always find the circumference of a circle as long as you know the diameter or the radius.
Here we have a circle with a given diameter of :
To find its circumference, multiply that measurement times :
We did not select the diameter randomly. To three decimal places, that circumference of the earth's equator.
The Encyclopedia Britannica tells us that a historic Round Table, rumored to be King Arthur's, has a radius of . To find the circumference of the circle that is King Arthur's table, we use the radius formula:
That is a massive table. Arthur supposedly gathered knights, though, so with all men gathered around, each had only centimeters of table edge to himself. They would have been elbow to elbow, those knights.
You can also find circumference with the area of a circle.
That same equation, , can also be used to find the diameter of a circle if you know circumference. Just divide both sides by the irrational number .
Suppose you are told the circle's circumference is . What is the diameter of the circle?
No, that diameter is not random; it is the size of the sarsen stone ring at Stonehenge.
The circumference equation using radius, , can also be used to find the radius of the circle if you know circumference.
Say we have a circle with a circumference of ; what is its radius? We will again divide both sides by , but we also need to eliminate the , so divide both sides by :
Of course, that is not a random number. That is the size of Notre Dame Cathedral's famed South Rose Window. That is a huge big stained glass window!
This lesson has provided you with lots of information the circumference of circles and a way to find any the measure of any one part if you have another measurement. Along the way, you also learned a little geography and history, which may also come in handy to you.
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