Area A car's rear windshield wiper rotates \( 125^{\circ} \). The total length of the wiper mechanism is 25 inches and the length of the wiper blade is 14 inches. Find the area wiped by the wiper blade.

We can think of the wiper blade as moving in a circular arc. Its motion sweeps out a “ring‐sector” (the region between two circular sectors) as it rotates. Step 1. Find the two radii. • The wiper mechanism is 25 inches long. This is the distance from the pivot to the inner end of the blade. • The blade itself is 14 inches long. So the outer edge of the blade is 25 + 14 = 39 inches from the pivot. Step 2. Write the formula for the area of a circular sector. For a circle of radius r swept by an angle θ (in degrees) the area is   Area = (θ/360)·π·r² Step 3. Find the areas of the outer and inner sectors. • Area of the outer sector (radius = 39):   A_outer = (125/360)·π·(39²) • Area of the inner sector (radius = 25):   A_inner = (125/360)·π·(25²) Step 4. Find the area swept by the wiper blade. This is the difference between the outer and inner sectors:   Area_wiped = A_outer – A_inner   = (125/360)·π·(39² – 25²) Step 5. Compute the numbers. First, calculate the squares:   39² = 1521  and  25² = 625 So, 39² – 25² = 1521 – 625 = 896. Thus,   Area_wiped = (125/360)·π·896 Simplify the fraction (notice that 125/360 can be simplified by dividing numerator and denominator by 5):   125/360 = 25/72. So,   Area_wiped = (25/72)·π·896 Multiply 25 by 896:   25 × 896 = 22,400 Thus,   Area_wiped = (22,400π)/72 Divide numerator and denominator by 8:   22,400 ÷ 8 = 2800  and  72 ÷ 8 = 9. So,   Area_wiped = (2800π)/9 square inches Step 6. Write the final answer. The area wiped by the wiper blade is (2800π)/9 square inches. (In decimal form this is approximately 977.38 square inches.) Thus, the answer is:   Area = (2800π)/9 square inches.