Question

A certain car's windshield wiper has a total length of 22 inches. As the wiper pivots it clears a sector with a central angle of 120 degrees. If only 18 inches of the wiper cleans the windshield, what is the area (in exact form) of the windshield that is wiped during each swing? 468π inches squared 156π inches squared 160π inches squared 108π inches squared

Answer 1

Answer: 108π inches squared

Explanation:

Formula : Area of sector =
`(\theta)/(360^(\circ))*\pi r^2`

where , r= radius and
`\theta =`

Given : A certain car's windshield wiper has a total length of 22 inches. As the wiper pivots it clears a sector with a central angle of 120 degrees.

If only 18 inches of the wiper cleans the windshield, then we take radius of the range of wiper cleaining = 18 inches

The area of the windshield that is wiped during each swing = Area of the sector made by wiper of with a central angle of 120 degrees.

`=(120)/(360)*\pi (18)^2\\\\=(18^2)/(3)\pi=(18*6)/(1)\pi=108\p\text{ inches}^2`

Hence, the area (in exact form) of the windshield that is wiped during each swing is 108π inches squared.