Unit 5B ­ Circumference and Arc Length p.1.notebook
March 08, 2012
Definition
• circumference – the distance around a circle. Mar 14­7:26 AM
Theorem: Circumference of a Circle
• The circumference C of a circle is C = πd or C = 2πr, where d is the diameter of the circle and r is the radius of the circle. Mar 14­7:26 AM
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Unit 5B ­ Circumference and Arc Length p.1.notebook
March 08, 2012
Example 1
• Find the circumference of a circle with a radius of 6 centimeters.
• Find the radius of a circle with a circumference of 31 meters.
2. C = 2πr
• C = 2πr
31 = 2pr
C = 2π(6)
31/2p = r
C = 12p cm
r » 4.93 meters C » 37.70 cm Mar 14­7:26 AM
Try This!
• Find the circumference of a circle with a radius of 9 in.
• Find the radius of a circle with a circumference of 52 in.
• about 56.55 inches
• about 8.28 inches
Mar 14­7:26 AM
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Unit 5B ­ Circumference and Arc Length p.1.notebook
March 08, 2012
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). Mar 14­7:26 AM
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
Mar 14­7:26 AM
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Unit 5B ­ Circumference and Arc Length p.1.notebook
March 08, 2012
Mar 14­7:26 AM
Example 2
• Find the length of arc AB. or
≈ 4.36 cm
Mar 14­7:26 AM
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Unit 5B ­ Circumference and Arc Length p.1.notebook
March 08, 2012
Try This!
• Find the length of arc CD. ≈ 6.11 cm
Mar 14­7:26 AM
Example 3
• Find the circumference of the circle. Let’s set up a proportion!
C = 22.92 meters
Mar 14­7:26 AM
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Unit 5B ­ Circumference and Arc Length p.1.notebook
March 08, 2012
Example 4
Hint: Set up a proportion!
Mar 14­7:26 AM
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