Answer:
175 square inches
Step-by-step explanation:
Area wiped by the wiper blade = Area covered by the whole wiper mechanism - Area that is not being wiped.
Where area of a sector of 125°....Area = 1/2.r^2.theta....but with theta in radians
Area covered of the whole wiper mechanism;
= 1/2 × 25^2 × (25pi/36)...in which (25pi/36) is 125° in radians..
=217.014pi
Area that is not being wiped;
= 1/2 × (25 - 14)^2 × (25pi/36)
= 42.014pi
Area wiped by the wiper blade
217.014 - 42.014
Area = 175 square inches
The area that is wiped by the blade is required.
The area wiped by the blade is [tex]549.78\ \text{inches}^2[/tex]
[tex]\theta[/tex] = Angle of sweep = [tex]125^{\circ}[/tex]
[tex]r_1[/tex] = Distance from the start of the mechanism to the tip of the blade = 25 inches
[tex]r_2[/tex] = Distance from the start of the mechanism to the beginning of the tip = [tex]25-14=11\ \text{inches}[/tex]
Area of sector of circle is
[tex]\dfrac{\theta}{360}\pi r^2[/tex]
Area of the wiped region would be
[tex]A=\dfrac{\theta}{360}\pi r_1^2-\dfrac{\theta}{360}\pi r_2^2\\ =\dfrac{\theta}{360}\pi (r_1^2-r_2^2)\\ =\dfrac{125}{360}\pi(25^2-11^2)\\ =175\pi =549.78\ \text{inches}^2[/tex]
The area wiped by the blade is [tex]549.78\ \text{inches}^2[/tex]
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