Answer:
The are cover in one cycle is 1036.7 square inches.
Step-by-step explanation:
Consider the provided information.
The blade of a windshield wiper sweeps out an angle of 135° in one cycle. The base of the blade is12 inches from the pivot point and the tip is 32 inches from the pivot point.
The area of a sector is: [tex]\frac{1}{2}r^2\theta[/tex] where θ is in radians.
First Converting 135º to radians, we get 3π/4.
The area of the region swept out by the wiper blade = (Area cover by tip) - (area of blade).
[tex]Area = \frac{1}{2}(32)^2\times \frac{3\pi}{4} -\frac{1}{2}(12)^2\times \frac{3\pi}{4}\\\\Area = \dfrac{3\pi}{8}(32^2 - 12^2) \approx1036.73[/tex]
The are cover in one cycle is 1036.7 square inches.
