Q15
1 markMCQSection A

  1. The hour hand of a clock is 7 cm long. The angle swept by it between 7:00 a.m. and 8:10 a.m. is : (a) (354)°\left(\frac{35}{4}\right)° (b) (352)°\left(\frac{35}{2}\right)° (c) 35°35° (d) 70°70°

Areas Related to Circles
Angle swept by clock hand

Options

(A)(354)°\left(\frac{35}{4}\right)°
(B)(352)°\left(\frac{35}{2}\right)°
(C)35°35°
(D)70°70°
Official Answer

(c) 35°35°, since the hour hand moves at 0.5°0.5° per minute and 70 minutes have elapsed, giving 70×0.5°=35°70 \times 0.5° = 35°.

hour handangle swept0.5 degree per minute360 in 12 hours70 minutesclock35 degreesrate of rotation

Marking Scheme

  • 11 mark for correct option (c) 35°.
  • 2Expected working: rate = 360°/(12×60)=0.5°/min360°/(12\times 60) = 0.5°/\text{min}; time = 70 min; angle = 70×0.5°=35°70 \times 0.5° = 35°.
  • 3The 7 cm length is a distractor and should be ignored for the angle.

Hint

The hour hand turns 360°360° in 12 hours = 0.5°0.5° per minute. The interval is 70 minutes.

Quick Oral Answer

The hour hand covers 360 degrees in 12 hours, so 0.5 degrees each minute; from 7:00 to 8:10 is 70 minutes, giving 70 times 0.5, which is 35 degrees.

Analysis & Explanation

Tests the concept of angular speed of a clock hand to find the angle swept over a given time interval.


Concept

  • The hour hand completes 360° in 12 hours (720 minutes), so its speed is 360°/720=0.5°360°/720 = 0.5° per minute.
  • The time from 7:00 a.m. to 8:10 a.m. is 1 hour 10 minutes = 70 minutes.
  • Angle swept = 70×0.5°=35°70 \times 0.5° = 35°.

Common mistakes

  • Using the minute hand's speed (6°/min6°/\text{min}) by mistake instead of the hour hand's.
  • Being distracted by the '7 cm' hand length, which is irrelevant to the angle swept (it would only matter for arc length travelled by the tip).

Common Mistakes

  1. 1Using 1°1° per minute (giving 70°70°) — that ignores that the hour hand turns only 0.5°0.5° per minute.
  2. 2Trying to use the 7 cm length, which is irrelevant to the angle and only matters for area/arc questions.
  3. 3Miscounting the time interval as 1 hour (60 min) and getting 30°30° instead of accounting for the extra 10 minutes.

Interesting Facts

The hour hand moves 0.5°0.5° per minute while the minute hand moves 6°6° per minute — exactly 12 times faster — which is why the two hands overlap 11 times every 12 hours.

In half an hour the hour hand moves 15°15°, which is why at 6:30 it points midway between the 6 and the 7, not exactly at the 6.

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Frequently Asked Questions

How many degrees does the hour hand move per minute?

It moves 0.5°0.5° per minute, because it completes 360° in 12 hours (720 minutes), and 360÷720=0.5360 \div 720 = 0.5.

Why is the 7 cm length given if it is not used?

It is a deliberate distractor. The length matters only for the area or arc swept; the angle depends solely on time and the hand's rotation rate.

What is the time interval used in this problem?

From 7:00 a.m. to 8:10 a.m. is 1 hour 10 minutes, which equals 70 minutes.