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Radius, Diameter, and Circumference
Radius
The radius of a circle is a line segment that goes from the center point to a point on the circle. Thus, it goes halfway through the circle.
Diameter
The diameter of circle is a line segment that goes all the way across a circle through the center point.
Circumference
The circumference of a circle is the distance around the outside of the circle.
The radius, diameter, and circumference of a circle always have the same relationships. Thus, if you know one of these, you can calculate the other two.
The diameter is always twice as long as the radius.
This makes sense because the diameter is all the way across the circle while the radius is only halfway across.
When circumference is involved, the relationship is a little bit more complex because of the number π (Pi).
π (Pi) is a special number that occurs in circles.
Did you know that if you divide the circumference of any circle by its diameter you will always get the same exact number every time?
The number you get is called π (Pi) and is approximately equal to 3.14, but the decimal places actually keep going and going. Computers have calculated millions and even billions of digits to the number π, but they haven’t been able to find the end of it yet. When you use π in a problem, typically you can just remember π is approximately 3.14.
There are three formulas you can use when dealing with the circumference:
In these formulas, C = circumference, r = radius, and d = diameter
1) Use the formula given below to find the circumference when you know the radius.
C = 2 x π x r
2) Use the formula given below to find the circumference when you know the diameter.
C = π x d
3) Use the formula given below to find the diameter when you know the circumference.
d = C ÷ π
Let's take a look at some examples:
Find the radius, diameter, and circumference of each circle.
1.
Radius = 4 inches
Remember, the radius goes halfway across the circle.
The diameter is always twice as long as the radius.
d = 2 x r
d = 2 x 4 = 8.
Hence, the diameter is 8 inches.
For the circumference, we need to choose a formula. It’s usually better to use the information we are given (instead of the information we figured out ourselves  just in case we made a mistake).
The first formula C = 2 x π x r has r in it, so we will start with that formula and substitute in the information we know.
C = 2 x π x r
This formula says we must multiply 2 times Pi (3.14) times the radius
C ≈ 2 x 3.14 x 4
Then we just need to multiply:
C ≈ 25.12 in.
Hence, the circumference is ≈ 25.12 inches.
2.
Diameter = 6 feet (as shown in the above picture)
Remember, the diameter goes all the way across the circle through the center point.
The diameter is always twice as long as the radius.
So if our diameter (d)is 6 feet, the radius (r) must be half as long as that.
d ÷ 2 = r
6 ÷ 2 = 3
Hence, the radius is 3 feet long.
For the circumference, we need to choose a formula.
The first formula C = π x d has d in it,
So we will start with that formula and substitute in the information we know.
C = π x dThis formula says we must multiply Pi (3.14) by the diameter.
C ≈ 3.14 x 6Then we just need to multiply:
C ≈ 18.84 ft.Hence,the circumference is ≈ 18.84 ft.
3.
We know that the circumference = 6.28 meters because we are told this, but we need to find the diameter or radius.
The formula given below should help us do that:
d = C ÷ πThis formula says that to find the diameter, we must take the circumference and divide it by Pi (3.14)
Do the math and we get:
d ≈ 6.28 ÷ 3.14
d ≈ 2 meters
Now that we know the diameter, it’s easy to find the radius.
The diameter is twice as long as the radius, so the radius is half as long as the diameter.
d ÷ 2 = r
2 ÷ 2 = r
1 = r
Hence, the radius is 1 meter long.
This answer makes sense. If halfway across the circle is 1 meter, all the way across is 2 meters.
These are the parts of circle.
Radius  A line segment that goes from the center point to a point on the circle. Thus, it goes halfway through the circle. 

Diameter  A line segment that goes all the way across a circle through the center point. 

Circumference  The distance around the outside of the circle. 
Remember following points to find radius, diameter, and circumference:
1. The diameter is always twice as long as the radius.
2. Important formulas:
1) Use the formula given below to find the circumference when you know the radius.
C = 2 x π x r
2) Use the formula given below to find the circumference when you know the diameter.
C = π x d
3) Use the formula given below to find the diameter when you know the circumference.
d = C ÷ π
3. π (Pi) is a special number that occurs in circles. Its decimal places keep going and going, but we can use the approximation 3.14. So, in calculations, think π ≈ 3.14.