A car has two wipers which do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle of 120°. Find the total area cleaned at each sweep of the two blades.
Generated by claude-sonnet-4-6 · 2026-06-15 10:37 · grounding rag
Model Answer
Given: radius (r) = 21 cm, angle (θ) = 120°, π = 22/7
Area cleaned by one wiper (one sector):
$$\text{Area} = \frac{\theta}{360} \times \pi r^2 = \frac{120}{360} \times \frac{22}{7} \times 21 \times 21$$
$$= \frac{1}{3} \times \frac{22}{7} \times 441 = \frac{1}{3} \times 1386 = 462 \text{ cm}^2$$
Total area cleaned by two wipers:
$$= 2 \times 462 = \mathbf{924 \text{ cm}^2}$$
Source: Areas Related to Circles, Chapter 11, Section 11.1
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Explanation
- Use the sector area formula: $\frac{\theta}{360} \times \pi r^2$. Since the two wipers do not overlap, simply multiply the single wiper's area by 2.
- Note: The textbook Q11 uses r = 25 cm and 115°, but this question uses r = 21 cm and 120° — apply the same method with the given values.
- Show each step clearly; examiners award marks for formula, substitution, and final answer.