An automobile 10 inch windshield wiper blade rotates through an angle of 60 degrees. What is the Area of coverage of the wiper blade?

Question

mathstudent55 · Answer

|dw:1397061930356:dw|
What you need to do is to find the area of a sector of a circle with 10-in. radius and a central angle of 60 degrees.

anonymous · Answer

If you know the formula for the area of a circle and you know how many degrees are in a circle, you can answer this. 

The problem is solved by breaking up with windshield wiper into 2 parts: the entire 10 inch wiper and its smaller 1 inch "base" (which contains no rubber). Each of these pieces swipes out a 60 degree chunk of circle (like one 10 inch "long" slice of pie and one 1 inch long slice). To get the area of the 9 inch region, simply subtract the area of the smaller 1 inch region from the area of the larger 10 inch region. 

The area of a circle is pi*r^2, so the area of each 60 degree region is equal to (60/360)pi*r^2. 

For a 10 inch radius, this comes to 52.36 square inches, and for a 1 inch radius, the area is 0.52 square inches. Thus, the area of the 9 inch swath is 52.36 - 0.52 = ? square inches