7-2 Sectors of Circles Objective: To find the arc length of a sector of a circle and to solve problems involving apparent size.

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Presentation transcript:

7-2 Sectors of Circles Objective: To find the arc length of a sector of a circle and to solve problems involving apparent size.

Sectors of Circles A sector of a circle, shaded below, it is the region bounded by a central angle and the intercepted arc.

Sectors of Circles 60° 6 cm Q R Example 1: The radius of a pizza is 6 cm. m  ROQ = 60 o. Find the area of the slice OQR. O

Sectors of Circles Example 2: The radius of a cake is 7 cm. m  ROP = 130 o. Find the area of the slices OPR. 130° 7 cm P R O

In general, the following formulas for the arc length s and area K of a sector with central angle . Arc Length and Area of a Sector of a Circle If  is in degrees, then the arc length and the area of a sector is: If  is in radians, then the arc length and the area of a sector is:

Arc Length s and Area K of a sector with central angle Unit of measurement Arc Length s Area K Degrees Radians

The arc length is: Area: Find the arc length and area of the sector r=9 30◦ s

A satellite orbits 400 miles above the earth. If the radius of the earth is 4000 miles and  BDC = 50° how many miles does the satellite cover? Relationships between Angles and Circles TRY IT IN RADIANS!!!!! CAUTION: NO LLORENS

Miss Keyvan has brought in a treat for Pi Day. Since Mr. Llorens is in wrestling season, he is watching his calorie intake and decides to eat only the frosting off of one piece. If Miss Keyvan uses her geometric skill to cut the cake into 8 equal pieces and used a 14 in by 3 in pie pan to bake her cake, how many calories will Mr. Llorens have consumed if each square cm of frosting contains 3 calories? R ELATIONSHIPS BETWEEN A NGLES AND C IRCLES CAUTION: LEVEL POBUDA

ASSIGNMENT Textbook Pg. 265 #13, 14