01 · REAL WORLD CONCEPTS
Key Real-World Angle Rules
Clock Minute Hand
Minute Hand Speed
Moves 360° in 60 minutes ⟹ 6° per minute. In 5 minutes, θ = 5 × 6° = 30°.Car Wipers
Dual Car Wipers
Total area swept by 2 non-overlapping wipers = 2 × [(θ / 360°) × πr²].Umbrella Ribs
Equal Sectors
If an umbrella has 8 equal ribs, central angle for 1 sector = 360° / 8 = 45°.02 · SOLVED NCERT EXAMPLES
Step-by-Step Problem Solving
EXAMPLE 1 · CLOCK MINUTE HAND
The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
In 60 minutes, minute hand rotates 360°. In 5 minutes, θ = (360° / 60) × 5 = 30°.
Radius r = 14 cm.
Area = (30° / 360°) × (22/7) × 14 × 14
Area = (1 / 12) × 22 × 2 × 14 = (22 × 28) / 12 = 154 / 3 = 51.33 cm²
Area = (1 / 12) × 22 × 2 × 14 = (22 × 28) / 12 = 154 / 3 = 51.33 cm²
EXAMPLE 2 · CAR WIPERS
A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find total area cleaned at each sweep.
Given: blade length r = 25 cm, angle θ = 115°, number of wipers = 2.
Area by 1 Wiper = (115° / 360°) × (22/7) × 25 × 25
Total Area (2 Wipers) = 2 × (115° / 360°) × (22/7) × 625
Total Area = (230 / 360) × (22/7) × 625 = 158125 / 126 = 1254.96 cm²
Total Area (2 Wipers) = 2 × (115° / 360°) × (22/7) × 625
Total Area = (230 / 360) × (22/7) × 625 = 158125 / 126 = 1254.96 cm²
03 · QUICK SUMMARY
Key Takeaways
01
Minute hand rotates 6° per minute (360° in 60 mins).
02
Always multiply single sector area by the number of blades/ribs when applicable.
03
Keep exact fractions (e.g. 154/3 cm²) for board exams unless decimal is specified.