Question

The total arm and blade of a windshield wiper is 15 in. long and rotates back and forth through an angle of 98°. The shaded region in the figure is the portion of the windshield cleaned by the ​10-in. wiper blade. What is the area of the region​ cleaned?

Answer 1

The area of the portion of the windshield cleaned by the 10-in wiper blade is 106.85in² .

We have been provided that the Length of blade is 15 inches and the Angle of rotation = 98°

We are required to calculate the area of the portion of the windshield cleaned by the 10-in wiper blade.

We have to solve this by using area of a sector.

Area of a sector = ½r²θ

where θ is in radians.

So, angle of rotation (98°) must first be converted to radians

Converting 98º to radians, we get

98×π/180 = 49π/90

The area of the region swept out by the wiper blade

= (area of the sector where r = 15 and θ = 49π/90) - (area of the sector where r = (15-10) and θ = 49π/90).

So, Area = ½×15²×49π/0 - ½×5²×49π/90

= ½×49π/90(15²-10²)

= 49π/180× (225 - 100)

= 49π/180 × 125

= 1225π/36

Area = 106.8472in²

=106.85 in²

Hence, the area of the portion of the windshield cleaned by the 10-in wiper blade is 106.85in²

To know more about area of a sector- brainly.com/question/7512468

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