The minute hand of a clock is 21 cm long. Find the distance moved by its tip in 20 minutes, and the perimeter of the sector it sweeps. (Use π = 22/7)
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Write what is given and what is to be found Given: length of the hand r = 21 cm, time 20 minutes. To find: the arc length and the perimeter of the sector.
2 · Draw the figure Circle (the clock face) with centre O. Radii OA and OB show the hand at the start and the end. Mark ∠AOB.
3 · Write the formula or theorem Angle in 20 minutes = 20 × 6° = 120°. Arc length = (θ/360) × 2πr.
4 · Find the arc length l = (120/360) × 2 × (22/7) × 21 = (1/3) × 132 = 44 cm.
5 · Find the perimeter Perimeter of the sector = 2r + l = 42 + 44 = 86 cm.
6 · Check and box the answer The tip moves 44 cm; the sector's perimeter is 86 cm. Check: 44 cm is one third of the full 132 cm.
Scoring tip: Convert the time into an angle first (6° per minute). Most wrong answers come from using 20 as the angle.
