Question

The top and bottom ends of a windshield wiper blade are R = 24 in. and r = 14 in., respectively, from the pivot point. While in operation, the wiper sweeps through 135°. Find the area swept by the blade. (Round your answer to the nearest whole number.)

Answer 1

Answer:

Area swept by the blade = 448$in^{2}$

Step-by-step explanation:

The arc the wiper wipes is for 135 degrees angle.

So, find area of sector with radius 24 inches. And the find area of arc with r=14 inches.

Then subtract the area of sector with 14 inches  from area of sector with radius as 24 inches.

So, area of sector with r=24 in =$\frac{135}{360} *\pi *24^{2}$

Simplify it,

                                                  =216$\pi$

Now, let's find area of sector with radius 14 inches

Area of sector with r=14 in = $\frac{135}{360} *\pi *14^{2}$

Simplify it

                                          =73.5$\pi$

So, area swept by the blade = 216$\pi$ -73.5$\pi$

Simplify it and use pi as 3.14.....

Area of swept =678.584 - 230.907

                               =447.6769

Round to nearest whole number

So, area swept by the blade = 448$in^{2}$