1. The tip of the minute hand travels 8.377 inches in 10 minutes.
2. The tip of the minute hand travels 33.929 inches in 40.5 minutes.
3. The tip of the minute hand travels 163.2628 inches in 3.25 hours.
Explanation:
- On any clock, in 60 minutes the minute hand rotates 360° degrees, so for every 10 minutes, the minute hand rotates an angle of 60°.
- So first, we calculate the angles rotated in 10 minutes, 40.5 minutes and 3.25 hours.
- For 10 minutes, the angle rotated is 60°. For every minute, the minute hand rotates an angle of 6° so for half a minute it covers 3°. For 40.5 minutes, it rotates 4 × 60° + 3° = 243°. 3.25 hours equals 195 minutes, angle rotated = 19.5 × 60° = 1170°.
- Arc length is calculated by using the formula 2πr × (θ/360). r = 8 inches.
- Arc length for 60° = 2π×8× (60/360) = 8.377 inches. Arc length for 243° = 2π×8× (243/360) = 33.929 inches. Arc length for 1170° = 2π×8× (1170/360) = 163.3628 inches.
