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

Sectors of Circles Example 2: The radius of a cake is 7 cm. If the area of sector ROP is 55.59 cm^2. Find the central angle of the sector OPR. R 7 cm O P

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

Example 3: A sector of a circle has an area of 30 square inches and central angle 3π/4 radians. Find its arc length.

Homework Textbook Pg. 265 #14