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Circumference and Diameter

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.

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Circumference and Diameter

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  1. Circumference and Diameter 1/31/2006

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. Examples • Example 1: The radius of a circle is 2 inches. What is the diameter? • d = 2 · r • d = 2 · (2in) • d = 4in

  8. 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

  9. 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

  10. 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

  11. 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

  12. Homework • Pg. 242 #1-5, 44-52 • GLE “Component 1.2: Understand and apply concepts and procedures from measurement.“ • Shortly before class ends, we will review problem number five from your assignment. Have it ready to look over.

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