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?

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

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