How to Work out the Circumference of a Circle
Draw a "radius" on the circle., Draw a "diameter" across the circle., Understand π ("pi")., Write down the definition of π as an algebra problem., Change this problem so you are solving for C, circumference., Plug in the numbers to solve for C. Now...
Step-by-Step Guide
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Step 1: Draw a "radius" on the circle.
Draw a line from the center of the circle to anywhere on the circle's edge.
This line is the "radius" of the circle, often written as just r in math equations and formulas.
Note: if your math problem doesn't tell you the length of the radius, you might be looking at the wrong section.
Check whether the sections for Diameter or Area make more sense for your problem. -
Step 2: Draw a "diameter" across the circle.
Extend the line you just drew so it reaches the circle edge on the other side.
You've just drawn a second radius.
The two radii stuck together have a length of "2 x the radius," written as 2r.
The length of this line is the "diameter" of the circle, often written d. , The π symbol, also written as pi.
It isn't a magical number that just happens to work in this kind of math problem.
Actually, the number π was originally "discovered" by measuring circles: if you measure the circumference of any circle (for instance with a tape measure), and then divide by the diameter, you'll always end up with the same number.
This number is unusual because it can't be written out as a simple fraction or decimal.
Instead, we can round to a "close enough" number like
3.14.
Even the π button on a calculator doesn't use the exact value of π, although it is close enough. , As explained above, π just means "the number you get when you divide the circumference by the diameter." In the form of a math formula: π = C / d.
Since we know the diameter equals 2 x the radius, we can also write this as π = C / 2r.
C is just a shorter way of writing "circumference."
We want to find out what the circumference is, which is C in this math problem.
If you multiply both sides by 2r you get π x 2r = (C / 2r) x 2r, which is the same as 2πr = C You might have written the left side as π2r, which is also correct.
People like to move the numbers in front of the symbols just so the equation is easier to read, and this doesn't change the result of the equation.
In a math equation, you can always multiple the left side and the right side by the same amount and still end up with a correct equation. , Then replace π with
3.14, or use a calculator's π button to get a more accurate answer.
Multiply 2πr together using these numbers.
The answer you get is the circumference.
For example, if the radius is 2 units long, then 2πr = 2 x (3.14) x (2 units) =
12.56 units = the circumference.
In the same example, but using a calculator's π button for better accuracy, you'll get 2 x π x 2 units =
12.56637... units but unless instructed otherwise by your teacher, you can round the number to
12.57 units. -
Step 3: Understand π ("pi").
-
Step 4: Write down the definition of π as an algebra problem.
-
Step 5: Change this problem so you are solving for C
-
Step 6: circumference.
-
Step 7: Plug in the numbers to solve for C. Now we know that 2πr = C. Look back at the original math problem to see what r (the radius) equals.
Detailed Guide
Draw a line from the center of the circle to anywhere on the circle's edge.
This line is the "radius" of the circle, often written as just r in math equations and formulas.
Note: if your math problem doesn't tell you the length of the radius, you might be looking at the wrong section.
Check whether the sections for Diameter or Area make more sense for your problem.
Extend the line you just drew so it reaches the circle edge on the other side.
You've just drawn a second radius.
The two radii stuck together have a length of "2 x the radius," written as 2r.
The length of this line is the "diameter" of the circle, often written d. , The π symbol, also written as pi.
It isn't a magical number that just happens to work in this kind of math problem.
Actually, the number π was originally "discovered" by measuring circles: if you measure the circumference of any circle (for instance with a tape measure), and then divide by the diameter, you'll always end up with the same number.
This number is unusual because it can't be written out as a simple fraction or decimal.
Instead, we can round to a "close enough" number like
3.14.
Even the π button on a calculator doesn't use the exact value of π, although it is close enough. , As explained above, π just means "the number you get when you divide the circumference by the diameter." In the form of a math formula: π = C / d.
Since we know the diameter equals 2 x the radius, we can also write this as π = C / 2r.
C is just a shorter way of writing "circumference."
We want to find out what the circumference is, which is C in this math problem.
If you multiply both sides by 2r you get π x 2r = (C / 2r) x 2r, which is the same as 2πr = C You might have written the left side as π2r, which is also correct.
People like to move the numbers in front of the symbols just so the equation is easier to read, and this doesn't change the result of the equation.
In a math equation, you can always multiple the left side and the right side by the same amount and still end up with a correct equation. , Then replace π with
3.14, or use a calculator's π button to get a more accurate answer.
Multiply 2πr together using these numbers.
The answer you get is the circumference.
For example, if the radius is 2 units long, then 2πr = 2 x (3.14) x (2 units) =
12.56 units = the circumference.
In the same example, but using a calculator's π button for better accuracy, you'll get 2 x π x 2 units =
12.56637... units but unless instructed otherwise by your teacher, you can round the number to
12.57 units.
About the Author
Elizabeth Sanders
Enthusiastic about teaching crafts techniques through clear, step-by-step guides.
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