circumference and areas of circles lesson 11.5 geometry honors objective: know and use the formulas...
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Circumference and Areas of Circumference and Areas of CirclesCircles
Lesson 11.5Lesson 11.5Geometry HonorsGeometry Honors
Objective: Know and use the Objective: Know and use the formulas for the Circumference formulas for the Circumference
and Areas of Circlesand Areas of Circles
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Lesson Focus
In this lesson, the formulas for circumference and area of a circle are stated. These formulas can be understood by using facts that have been developed about areas of regular polygons.
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SummaryBasic Terms
CircumferenceThe perimeter of or distance around a circle.
Area of a CircleThe area of a disk (the region inside a circle) is πr2 when the circle has radius r.
πAn irrational number that is the ratio of the circumference of a circle to its diameter.
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Area of a Circle
Area, A = πr2
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Circumference
Circumference, C = 2πr = πd
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Pi
• Leave answers in π form unless an approximation is specified.• The exact circumference or exact area of a circle requires that π be approximated.• π is an irrational number is not the ration of two integers, as the quotient 22/7 suggests. • In the expression C/d, d is rational, C is not, and vice versa.
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Practice
1. What is the ratio of the circumference to the diameter for each circle?
2. A circle has a radius of 15. What is the diameter, circumference, and area of the circle?
3. A circle has a diameter of 8. What is the radius, circumference, and area of the circle?
4. A circle has a circumference of 26π. What is the radius, diameter, and area of the circle?
5. A circle has an area of 100π. What is the radius, diameter, and circumference of the circle?
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Written Exercises
Problem Set 11.5, p.448: # 2 – 16 (even) Handout: 11-5