Section 7.4: Circumference and Area of a Circle

1
Section 7.4Circumference and Area of a Circle

• Postulate 22 The ratio of the circumference of
  a circle to the length of its diameter is a
  unique positive constant.
• ? (pi) is the ratio between the circumference C
  and the diameter length of any circle thus ?
  C/d in any circle.

2
Length of an Arc

• Distance between the endpoints of the arc as
  though it was measured along a straight line.
• Theorem 7.4.2 In a circle whose circumference
  is C, the length l of an arc whose degree
  measure m is given by l m ?C
• 360
• Example 4 p. 368 Figure 7.47
• Limits an approximation of an upper or lower
  numerical value. See Example 5

3
Area of a Circle

• Theorem 7.4.3 The area A of a circle whose
  radius has length r is given by A ?r²
• Ring A plane figure bounded by concentric
  circles.
• Example 8 p. 370