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Pre-Calc Exam Notes 95

# Pre-Calc Exam Notes 95 - Area of a Sector Section 4.3 95...

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Area of a Sector Section 4.3 95 4.3 Area of a Sector r θ Figure 4.3.1 In geometry you learned that the area of a circle of radius r is π r 2 . We will now learn how to find the area of a sector of a circle. A sector is the region bounded by a central angle and its intercepted arc, such as the shaded region in Figure 4.3.1. Let θ be a central angle in a circle of radius r and let A be the area of its sector. Similar to arc length, the ratio of A to the area of the entire circle is the same as the ratio of θ to one revolution. In other words, again using radian measure, area of sector area of entire circle = sector angle one revolution A π r 2 = θ 2 π . Solving for A in the above equation, we get the following formula: In a circle of radius r , the area A of the sector inside a central angle θ is A = 1 2 r 2 θ , (4.5) where θ is measured in radians. Example4.8 Find the area of a sector whose angle is π 5 rad in a circle of radius 4 cm. Solution: Using θ = π 5 and r = 4 in formula (4.5), the area A of the sector is A = 1 2 r 2 θ = 1 2 (4)
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