Circumference and Arc Length

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Circumference and Arc Length

• Section 6.7

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Essential Questions

• How do I find the circumference of a circle and
  the length of a circular arc?
• How do I use circumference and arc length to
  solve problems?

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Activator

• Find the measure of each arc.

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41? 110? 250? 319?
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Definition

• circumference the distance around a circle.

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Theorem Circumference of a Circle

• The circumference C of a circle is C ?d or
  C 2?r, where d is the diameter of the circle
  and r is the radius of the circle.

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Example 1

1. Find the circumference of a circle with a radius
   of 6 centimeters.
2. Find the radius of a circle with a circumference
   of 31 meters.

2. C 2?r 31 2?r 31/2? r r ? 4.93
meters

• C 2?r
• C 2?(6)
• C 12? cm
• C ? 37.70 cm

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Try This!

1. Find the circumference of a circle with a radius
   of 9 in.
2. Find the radius of a circle with a circumference
   of 52 in.

1. about 56.55 inches
2. about 8.28 inches

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Definition

• arc length a portion of the circumference of a
  circle. You can use the measure of the arc (in
  degrees) to find its length (in linear units).

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Arc Length Corollary

• In a circle, the ratio of the length of a given
  arc to the circumference is equal to the ratio of
  the measure of the arc to 360º.

or
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Example 2

• Find the length of arc AB.

? 4.36 cm
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Try This!

• Find the length of arc CD.

? 6.11 cm
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Example 3

• Find the circumference of the circle.

Lets set up a proportion!
C 22.92 meters
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Example 4
Hint Set up a proportion!
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Summarizer

• What proportion can you use to find the arc
  length of a given arc?

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Homework