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.

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Presentation transcript:

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 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 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