Area of the region of the wiper?

Question

The top of a windshield wiper blade is 34 inches from the pivot point, while the bottom of the blade is 14 inches from the pivot point. The wiper sweeps through an angle of 135 degrees. To the nearest whole number, what is the area of the region cleared by the wiper?

 

Please answer showing steps on how to get answer.

The following answers were provided to choose from:

A.) 1,131 in^2

B.) 1,362 in^2

C.) 78,030 in^2

D.) None of the above

Answer 1

The formula for the area of a sector is (1/2)r²Θ, where Θ is in radians.  Converting 135º to radians, we get 3π/4.  The area of the region swept out by the wiper blade = (area of the sector where r = 34 and

Θ = 3π/4) - (area of the sector where r = 14 and Θ = 3π/4).

 

So Area = (1/2)(34²)(3π/4) - (1/2)(14²)(3π/4)

 

           =  (3π/8)(34² - 14²) = 1130.973355 in²  ≈ 1131 in².

 

The answer is "A".

 

 

 

 
≈