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# 9.6 Circles

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Chapter 9, Section 6: Circles

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### 9.6 Circles

1. 1. Chapter 9 Section 6: Circles March 11, 2009
2. 2. Find Circumference <ul><li>A Circle is the set of all points that are the same distance from a given point. </li></ul><ul><li>The given point is the CENTER of the circle. </li></ul><ul><li>Circumference : the distance around the circle. </li></ul>Center
3. 3. Inside the Circle <ul><li>Radius : a line segment that starts on the circle and ends at the center point. </li></ul><ul><li>Chord : segment whose end points are on the circle. </li></ul><ul><li>Diameter : a chord that passes through the center of the circle </li></ul>
4. 4. Pi or π <ul><li>Pi or π, pronounced “pie,” is the ratio of Circumference (or C) to Diameter (or d). </li></ul><ul><li>C = πd </li></ul><ul><li>C/d = π </li></ul><ul><li>Pi is constant = 3.14159265358979323846… </li></ul><ul><li>Pi as a fraction = 22/7 </li></ul><ul><li>Because every circle is the same, the ratio is always the same, which is why pi is a constant. </li></ul>
5. 5. Pi <ul><li>C = πd </li></ul><ul><li>If the d, or diameter, equals 1, then what is the Circumference (or C)? </li></ul><ul><li>C = π(1), C = π </li></ul>
6. 6. Find the circumference of the circle with a diameter of 6ft. <ul><li>C = πd  the formula </li></ul><ul><li>C (approx.) = 3.14(6ft)  Substitute </li></ul><ul><li>C = 18.84  Simplify! </li></ul>6 Feet
7. 7. Find the Circumference of Each Circle <ul><li>Diameter = 200 miles </li></ul><ul><li>Radius = 30 millimeters </li></ul><ul><li>Diameter = 2.8 inches. </li></ul>About 628 Miles About 188.4 mm About 8.8 inches
8. 8. Making Circle (Pie) Graphs <ul><li>A CENTRAL ANGLE is an angle whose vertex is the center of a circle. </li></ul><ul><li>There are 360 ° in a circle. </li></ul><ul><li>To make a Pie Graph, find the measure of each central angle by finding the proportion. </li></ul>
9. 9. Use proportions to find the measures of the central angles. <ul><li>Juan’s Weekly Budget : </li></ul><ul><li>Lunch (l) = 25% </li></ul><ul><li>Recreation (r) = 20% </li></ul><ul><li>Clothes (c) = 15% </li></ul><ul><li>Savings (s) = 40% </li></ul>Find the percentage of 360 ° to find the degree measurement of the central angles. L = 90 ° R = 72 ° C = 54 ° S = 144 °
10. 10. AT HOME <ul><li>Use a cup opening or cap to make your circles if you don’t have a compass. </li></ul>
11. 11. Blood Types of Population <ul><li>Tell me the degree measurements of the central angles if you were to make a Pie graph with this information. </li></ul>43% 5% 12% 40% Type O Type AB Type B Type A 155 ° 18 ° 43 ° 144 °
12. 12. Students at Western High School: Find Central Angles. <ul><li>Students at Western High School work in the following places; restaurants, 140; library, 15; auto shop, 60; retail stores, 75; and other places, 30. Round the measures of the central angles to the nearest degree. </li></ul>Restaurant: 158 ° Retail: 84 ° Auto Shop: 68 ° Other: 34 ° Library: 17 °
13. 13. Assignment #16: <ul><li>Pages 472-473: 1-24. Skip #20. </li></ul><ul><li>Remember, if you need a circle and have no compass, then use a cup from home and trace the outside. </li></ul>