It the wiper blade (and arm) made a full rotation, 2 circles would be formed.
One small circle with radius b, and a larger circle with radius a+b.
The areas of these 2 circles are respectively:
[tex]\pi b^2=\pi\cdot 5^2=25 \pi (in^2)[/tex] and
[tex]\pi (a+b)^2=\pi (14+5)^2=361\pi (in^2)[/tex]
120° is 1/3 of a complete angle 360° which form a circle, so the areas formed by the arm of length b, and the arm + the wiper blade (a+b) are:
[tex] \frac{25 \pi}{3}[/tex] and [tex] \frac{361\pi}{3} [/tex] in squared respectively.
the actual wiped area is [tex]\frac{361\pi}{3}-\frac{25 \pi}{3}= \frac{336\pi}{3}=112\pi \approx351.7 [/tex] (in squared)
Area of the window is 54*24= 1296 (in squared)
thus, the ratio of the wiped area to the whole area of the window is 351.7/1296=0.271
Converted to percentages, this is 27.1%
Answer: 27.1%
