A circular clock has a radius of 14 cm. Calculate the distance covered by the tip of the minute hand in 30 minutes, assuming it is positioned at the edge of the clock face? (Use π= 22⁄7)
- (a)44 cm
- (b)48 cm
- (c)46 cm
- (d)42 cm
Answer
Why
Correct — A. The minute hand goes once round the dial in 60 minutes, and its tip traces a circle of radius 14 cm.
Fraction of a turn: 30 ÷ 60 = 1⁄2
Full circumference: 2 × 22⁄7 × 14 = 88 cm
Half of it: 88 ÷ 2 = 44 cm → option (a)
Why the others are wrong
- (b)48 cm — 48 cm is 48 ⁄ 88 ≈ 0.545 of a turn, which the minute hand covers in about 32.7 minutes, not 30.
- (c)46 cm — 46 cm is 46 ⁄ 88 ≈ 0.523 of a turn, about 31.4 minutes of travel for the minute hand, not 30.
- (d)42 cm — 42 cm is 3 × 14, half a turn with π taken as 3. The stem fixes π = 22⁄7, which gives 44 cm.
Concept
The tip of a clock hand traces an arc whose radius is the hand's length. Arc length = (fraction of a full turn) × 2πr.
The minute hand turns 360° in 60 minutes, or 6° a minute, so 30 minutes is 180°: half the circumference, πr.
The stem puts the tip at the edge of the clock face. That is what makes the hand's length equal the clock's radius, 14 cm.
Key facts
- Minute hand: 360° in 60 minutes, or 6° per minute.
- Hour hand: 360° in 12 hours, or 0.5° per minute.
- Arc length = (θ ⁄ 360°) × 2πr.
Study next
Common traps
- Finding the area swept, ½ × 22⁄7 × 14² = 308 cm², when the question asks for distance along the edge.
- Using the full circumference, 88 cm, as though 30 minutes were a full turn.
The fraction-of-a-turn idea also sets 12 Sep 2025, 09:00, Quant Q.23: a quarter turn of a bicycle wheel of radius 35 cm covers 25% of its circumference, whatever the radius.
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