Circumference and Diameter

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Circumference and Diameter

• 1/31/2006

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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.

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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.

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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.
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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.
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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.
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Examples

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

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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

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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

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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

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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

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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.