Circumference and Diameter

1/31/2006

Circumference

A circle is a shape with all points the same distance from the center. It is named by the center.

The circle to the left is called circle A since the center is at point A.

Circumference

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 Pi to represent this value.

Circumference

The distance around a circle is called the circumference. The distance across a circle through the center is called the diameter. Pi 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 Pi.

Circumference

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.

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 where d is the diameter and r is the radius.

Examples

Example 1: The radius of a circle is 2 inches. What is the diameter?

d = 2 · rd = 2 · (2in)d = 4in

Examples

Example 2: The diameter of a circle is 3 centimeters. What is the circumference?

C = Pi · dC = 3.14 · (3cm)C = 9.42cm

Examples

Example 3: The radius of a circle is 2 inches. What is the circumference?

d = 2 · rd = 2 · (2in)d = 4inC = Pi · dC = 3.14 · (4in)C = 12.56in

Examples

Example 4: The circumference of a circle is 15.7 centimeters. What is the diameter?

C = Pi · d(15.7cm) = 3.14 · d15.7 cm ÷ 3.14 = dd = 5cm

Summary

The number Pi is the ratio of the circumference of a circle to the diameter.

The value of Pi is approximately 3.14. The diameter of a circle is twice the radius.

Given the diameter or radius of a circle, we can find the circumference.

We can also find the diameter (and radius) of a circle given the circumference.

The formula for diameter is d = 2 · r The formula for circumference is C = Pi · d