CDS 2026 (I) Elementary Mathematics, question 60

Topic: Mensuration

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Q60

The minute hand of a clock is 1515 cm long and sweeps an area of 15π cm215\pi\text{ cm}^{2} on the dial of the clock. How much angle does it describe during this period ?

  1. (a) 12∘12^{\circ}
  2. (b) 18∘18^{\circ}
  3. (c) 24∘24^{\circ}Correct answer
  4. (d) 30∘30^{\circ}

Solution.

Answer: (c) 24∘24^{\circ}

  1. The swept sector has area (θ/360∘)πr2\left( \theta/360^{\circ} \right)\pi r^{2}.
  2. Therefore (θ/360∘)π(15)2=15π\left( \theta/360^{\circ} \right)\pi(15)^{2} = 15\pi, giving θ=360×15/225=24∘\theta = 360 \times 15/225 = 24^{\circ}.