Question 151 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°.

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

Marking scheme

  1. 1.1 mark for correct option (c) 35°.
  2. 2.Expected 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°.
  3. 3.The 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.

Common mistakes

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

Analysis and 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).

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.

Question details

Q15 of 53 questions

Board
CBSE
Class
Class 10
Subject
Mathematics (Basic)
Year
2026
Section
Section A
Marks
1
Type
MCQ
Chapter
Areas Related to Circles
Topic
Angle swept by clock hand
Bloom's level
apply
Syllabus topic
Unit 5: Mensuration — Areas Related to Circles: Angle described by a rotating clock hand
Author
CBSE
Reviewed by
Padhantu Academic Team

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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.