Question

A car has a windshield wiper on the driver's side that has total arm length of 10 inches. It rotates

back and forth through an angle of 95 degrees. The shaded region below is the sector of the

windshield cleaned by the 7-inch wiper blade. What is the area of the sector cleaned?

795

total arm

10 in

wiper blade

7 in

Answer 1

75.44 Square Inches

Explanation:

The diagram of the problem is produced and attached.

To determine the area of the cleaned sector:

Let the radius of the larger sector be R

Let the radius of the smaller sector be r

Area of the larger sector
`=(\theta)/(360)X\pi R^2`

Area of the smaller sector
`=(\theta)/(360)X\pi r^2`

Area of shaded part =Area of the larger sector-Area of the smaller sector

`=(\theta)/(360)X\pi R^2-(\theta)/(360)X\pi r^2\\=(\theta \pi)/(360)X (R^2- r^2)`

From the diagram, R=10 Inch, r=10-7=3 Inch,
`\theta=95^\circ`

Therefore, Area of the sector cleaned

`=(95 \pi)/(360)X (10^2- 3^2)\\=75.44$ Square Inches`