Intro: Circumference of a Circle
This instructable will teach and demonsrtrate how to get the circumfrence of a circle.
Step 1: Pi?
If you measure the distance around a circle and divide it by the distance across the circle through the center, you will always come close to a particular value, depending upon the accuracy of your measurement. This value is approximately 3.14159265358979323846... We use the Greek letter (pronounced Pi) to represent this value. The number goes on forever. However, using computers, mathematicians have been able to calculate the value of to thousands of places. the point in the center is the center. I called it Point A.
Step 2: Diameter
The distance around a circle is called the circumference. The distance across a circle through the center is called the diameter. is the ratio of the circumference of a circle to the diameter. Thus, for any circle, if you divide the circumference by the diameter, you get a value close to . The picture I have is the relationship, the numbers expressed is the formula:
Where C is circumference and D is diameter. You can test this formula at home with a round dinner plate. If you measure the circumference and the diameter of the plate and then divide C by D, your quotient should come close to Pi . Another way to write this formula is: C = Pi * D where * means multiply. This second formula is commonly used in problems where the diameter is given and the circumference is not known (see the examples below).
Step 3: Radius
The radius of a circle is the distance from the center of a circle to any point on the circle. If you place two radii end-to-end in a circle, you would have the same length as one diameter. Thus, the diameter of a circle is twice as long as the radius. This relationship is expressed in the following formula: D = 2 * R ,(* = Multiply) where D is the diameter and R is the radius.
Step 4: Ready?
Circumference, diameter and radii are measured in linear units, such as inches and centimeters. A circle has many different radii and many different diameters, each passing through the center. A real-life example of a radius is the spoke of a bicycle wheel. A 9-inch pizza is an example of a diameter: when one makes the first cut to slice a round pizza pie in half, this cut is the diameter of the pizza. So a 9-inch pizza has a 9-inch diameter. Let's look at some examples of finding the circumference of a circle. In these examples, we will use Pi = 3.14 to simplify our calculations.
Step 5: Simplify It for Me!
Ok here is it simplified.
R(radius) is 1/2 the D(diameter) so D = R * 2
C(circumference) is the D(diameter) * Pi(3.14) so C = D * Pi(3.14)
Step 6: Practice Problem
Ok the R = 2 in.
so 2 * 2 = 4
so the D = 4
4 * 3.14 = 12.56
Step 7: More Practice
ok now we are going to do the opposite, go from the Circumference to the Diameter and then the Radius.
C = 43.96
D = C divided by 3.14
43.96 divided by 3.14 = 14, the Diameter
14 divided by 2 = 7, the radius.