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27 February, 05:36

The windshield of a car has a total length of arm and blade of 9 inches, and rotates back and forth through an angle of 93degrees. What is the area of the portion of the windshield cleaned by the 7 -in wiper blade?

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Answers (2)
  1. 27 February, 05:45
    0
    Answer:Area cleaned by the 7-in wiper blade=22

    72sq in

    Explanation: In a windshield the wiper moves in a semi circle. The angle in a semi circle is 180°

    Let A = Total area

    A = 2*9*3.1461 * (93/180)

    A=29.22squareinch

    Let a be area cleaned by the 7-inch wiper

    a=29.22 - 2 (9-7) * 3.1461 * (93/180)

    a=29.22 - 6.502

    a = 22.72sqin
  2. 27 February, 05:52
    0
    The area of the portion of the windshield cleaned by the 7-in wiper blade is 62.49 in²

    Explanation:

    Given

    Length of blade = 9 inches

    Angle of rotation = 93°

    We're to calculate the area of the portion of the windshield cleaned by the 7 -in wiper blade?

    We'll solve this by using area of a sector.

    Area of a sector = ½r²θ

    where θ is in radians.

    So, angle of rotation (93°) must first be converted to radians

    Converting 93º to radians, we get 31π/60

    The area of the region swept out by the wiper blade = (area of the sector where r = 9 and

    θ = 31π/60) - (area of the sector where r = (9-7) and θ = 31π/60).

    We're making use of 9-7 because that region is outside the boundary of the 7in blade

    So Area = ½*9²*31π/60 - ½*2²*31π/60

    Area = ½*31π/60 (9²-7²)

    Area = 31π/120 * (81 - 49)

    Area = 31π/120 * 32

    Area = 992π/120

    Area = 62.49151386765697 in²

    Area ≈ 62.49 in²

    Hence, the area of the portion of the windshield cleaned by the 7-in wiper blade is 62.49 in²
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