A car has two wipers which do not overlap. Each wiper has a blade of length 28 cm and sweeps through an angle of 120°. Find the total area cleaned at each sweep of the blades.
4928/3 cm² or 1642.67 cm²
Explanation
The area cleaned by each wiper forms a sector of a circle. Since the two wipers do not overlap, the total area cleaned at each sweep is the sum of the areas of the two sectors, which is simply twice the area cleaned by one wiper. We use the approximation 22/7 for π as instructed in the context.
Solution Steps
Step 1: Identify the shape and parameters: Each wiper sweeps a sector of a circle with radius r = 28 cm and angle θ = 120°.
Step 2: Formula for area of a sector: Area = (θ/360) × πr²
Step 3: Calculate area of one sector: Area = (120/360) × (22/7) × (28)² = (1/3) × (22/7) × 784 = 2464/3 cm²
Step 4: Calculate total area: Since there are two non-overlapping wipers, Total Area = 2 × (2464/3) = 4928/3 cm² 1642.67 cm²