Post on 12-Jan-2015
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Chapter 9Section 6:
Circles
March 11, 2009
Find Circumference
A Circle is the set of all points that are the same distance from a given point.
The given point is the CENTER of the circle. Circumference: the distance around the
circle.Center
Inside the Circle
Radius: a line segment that starts on the circle and ends at the center point.
Chord: segment whose end points are on the circle.
Diameter: a chord that passes through the center of the circle
Pi or π
Pi or π, pronounced “pie,” is the ratio of Circumference (or C) to Diameter (or d).
C = πd
C/d = π
Pi is constant = 3.14159265358979323846…
Pi as a fraction = 22/7 Because every circle is the same, the ratio is
always the same, which is why pi is a constant.
Pi
C = πd If the d, or diameter, equals 1, then what is
the Circumference (or C)? C = π(1), C = π
Find the circumference of the circle with a diameter of 6ft. C = πd the formula C (approx.) = 3.14(6ft) Substitute C = 18.84 Simplify!
6 Feet
Find the Circumference of Each Circle
Diameter = 200 miles
Radius = 30 millimeters
Diameter = 2.8 inches.
About 628 Miles
About 188.4 mm
About 8.8 inches
Making Circle (Pie) Graphs
A CENTRAL ANGLE is an angle whose vertex is the center of a circle.
There are 360° in a circle.
To make a Pie Graph, find the measure of each central angle by finding the proportion.
Use proportions to find the measures of the central angles.
Juan’s Weekly Budget: Lunch (l) = 25% Recreation (r) = 20% Clothes (c) = 15% Savings (s) = 40%
Find the percentage of 360° to find the degree
measurement of the central angles.
L = 90°
R = 72°
C = 54°
S = 144°
AT HOME
Use a cup opening or cap to make your circles if you don’t have a compass.
Blood Types of Population
Tell me the degree measurements of the central angles if you were to make a Pie graph with this information.
Type A
Type B
Type AB
Type O
40% 12% 5% 43%
144° 43° 18° 155°
Students at Western High School: Find Central Angles. 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.
Restaurant: 158°
Retail: 84° Auto Shop: 68°
Other: 34°
Library: 17°
Assignment #16:
Pages 472-473: 1-24. Skip #20.
Remember, if you need a circle and have no compass, then use a cup from home and trace the outside.