Chapter 8.5, Problem 41E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# In Exercises 41 and 42, round to two decimal places.A windshield wiper rotates through a 1200 angle as it cleans a windshield. From the point of rotation, the wiper blade begins at a distance of 4 in. and ends at a distance of 18 in. (The wiper blade is 14 in. in length.) Find the area cleaned by the wiper blade.

To determine

To find:

The area cleaned by the wiper blade.

Explanation

Formula:

Area of sector:

If r is the radius of the circle, the area A of a sector whose arc has degree measure m is given by

A=m360Ã—Ï€r2

Calculation:

To find the area cleaned by wiper blade, we have to subtract the area of inner sector with radius 4 in. from the area of outer sector with radius 18 in.

Area cleaned by wiper blade =AouterÂ sector-AinnerÂ sector

It is given that the wiper blade sweeps through an angle of 1200 as it cleans the windshield.

Hence the degree measure of arc is 1200.

Letâ€™s find the area of outer sector.

From the diagram, it is clear that the radius r1 of outer sector is 18 in.

Letâ€™s substitute the value of radius of outer sector and m=1200 to find the area of outer sector.

Asector=m360Ã—Ï€r12

AouterÂ sector=120360Ã—Ï€Ã—182

Simplify:AouterÂ sector=13Ã—Ï€Ã—324

Simplify: AouterÂ sector=108Ï€ in2.

Letâ€™s substitute the value of Ï€â‰ˆ3.14

AouterÂ sector=108Ã—3

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