Answer: 108π inches squared
Step-by-step explanation:
Formula : Area of sector = [tex]\dfrac{\theta}{360^{\circ}}\times\pi r^2[/tex]
where , r= radius and [tex]\theta =[/tex]
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.
[tex]=\dfrac{120}{360}\times\pi (18)^2\\\\=\dfrac{18^2}{3}\pi=\dfrac{18\times6}{1}\pi=108\p\text{ inches}^2[/tex]
Hence, the area (in exact form) of the windshield that is wiped during each swing is 108π inches squared.
