   Chapter 8.1, Problem 54E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Area of a Sector of a Circle In Exercises 53 and 54, use the following information. A sector of a circle is the region bounded by two radii of the circle and their intercepted arc (see figure). For a circle of radius r, the area A of a sector of the circle with central angle θ (in radians) is given by A = 1 2 r 2 θ .Windshield Wiper A car’s rear windshield wiper rotates 125 ° . The wiper mechanism has a total length of 25 inches and wipes the windshield over a distance of 14 inches. Find the area covered by the wiper.

To determine

To calculate: The area covered by the wiper if a car’s windshield wiper rotates through an angle of 125°. The total length of wiper mechanism is 25 in and it wipes the windshield over the distance of 14 in.

Explanation

Given Information:

A car’s windshield wiper rotates through an angle of 125°. The total length of wiper mechanism is 25 in and it wipes the windshield over the distance of 14 in. The area of a sector of a circle of radius r and central angle θ is A=12r2θ.

Formula used:

In order to convert the angle from degree to radian, multiply the angle by π radians180°.

Calculation:

Consider the figure of the car’s wiper which rotates through an angle of 125° and has 25 in radius.

Multiply angle 125° by π radians180° to find the angle in radians.

From above diagram, the area covered by the wiper can be calculated as:

A=12R2θx

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