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.