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Circumference and DiameterPowerPoint Presentation

Circumference and Diameter

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### 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 · r
- d = 2 · (2in)
- d = 4in

Examples

- Example 2: The diameter of a circle is 3 centimeters. What is the circumference?
- C = Pi · d
- C = 3.14 · (3cm)
- C = 9.42cm

Examples

- Example 3: The radius of a circle is 2 inches. What is the circumference?
- d = 2 · r
- d = 2 · (2in)
- d = 4in
- C = Pi · d
- C = 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 · d
- 15.7 cm ÷ 3.14 = d
- d = 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

- Created by Christopher Louck
- http://www.kent.k12.wa.us/staff/ChristopherLouck/math.htm
- Used by permission

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