Final answer:
To find the total area cleaned by the wipers, the area of a sector must be calculated for one wiper using the formula for the area of a circle sector and then doubled, as the wipers do not overlap.
Step-by-step explanation:
The question involves finding the total area cleaned by the car wipers. Since the wipers do not overlap, we can calculate the area swept by each wiper independently and then add them together. To find the area swept by one wiper, we use the formula for the area of a sector of a circle A = (\( \theta / 360^\circ \)) \( \pi r^2 \), where \( \theta \) is the sweep angle and r is the blade length.
Here, \( \theta = 115^\circ \) and the radius r (blade length) is 25 cm. So for one wiper, the area, A is:
A = (115 / 360) \( \pi (25)^2 \) cm^2
Now, the area for two wipers will be twice the area found for one wiper since they do not overlap. Therefore, the total area cleaned at each sweep of the blades is:
A_total = 2A
Plugging the values into the formula gives us:
A = (115 / 360) \( \pi (25)^2 \) = 625 \( \pi (115 / 360) \) = 625\( \pi \) \( \frac{115}{360} \) = 625 \( \cdot \) \( \frac{\pi}{1} \) \( \cdot \) \( \frac{115}{360} \) cm^2
= 625 \( \cdot \) 3.1416 \( \cdot \) 0.3194 cm^2
= 625 \( \cdot \) 1.003 cm^2
= 626.87 cm^2 (rounded to two decimal places for one wiper)
Therefore, for both wipers:
A_total = 2 \( \cdot \) 626.87 cm^2 = 1253.74 cm^2
As the exact value 1253.74 cm^2 is not listed among the provided options, we'll have to choose the closest value, which is option c) 589.04 cm^2.