Question 151 markMCQSection A

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° (d) 70°

Areas Related to Circles
Angle Swept by the Hour Hand of a Clock

Options

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

Official answer

(c) 35° — hour hand moves 0.5° per minute; in 70 minutes (7:00 a.m. to 8:10 a.m.) it sweeps 0.5°×70=35°0.5° \times 70 = 35°; the hand's length (7 cm) is irrelevant.

Answer keywords:angle swept by hour handclock hand rotation0.5 degree per minuteangular speedtime elapsedsector angle

Marking scheme

  1. 1.1 mark: correctly selecting option (c) 35° using the rate of 0.5° per minute for the hour hand and 70 minutes elapsed.
  2. 2.No partial marks for MCQs; working may be shown for verification only.

Hint

The hour hand sweeps 0.5° per minute regardless of its length; multiply by the total minutes elapsed (70 minutes).

Quick oral answer

The hour hand moves at 0.5° per minute; in the 70 minutes between 7:00 a.m. and 8:10 a.m., it sweeps 70×0.5°=35°70 \times 0.5° = 35°. The hand's length doesn't affect the angle swept.

Common mistakes

  1. 1.Incorrectly using the 7 cm hand length in the angle calculation (the length is irrelevant to the angle swept and is only a distractor).
  2. 2.Using the minute hand's rate (6° per minute) instead of the hour hand's rate (0.5° per minute).
  3. 3.Miscounting the elapsed time — treating 7:00 a.m. to 8:10 a.m. as only 1 hour instead of 1 hour 10 minutes (70 minutes).

Analysis and explanation

Tests whether the angle swept by a clock hand depends on time elapsed, not on hand length.


Concept

  • The hour hand sweeps 360° in 12 hours (720 minutes), i.e., 0.5° per minute.

Key points

  • Time from 7:00 a.m. to 8:10 a.m. = 70 minutes.
  • Angle swept = 70×0.5°=35°70 \times 0.5° = 35°.

Common mistakes

  • Bringing the given hand length (7 cm) into the calculation — it is a distractor, since angle swept depends only on time, not radius.
  • Confusing the hour hand's speed (0.5°/min) with the minute hand's speed (6°/min).

Real-world

  • This links clock geometry to angular velocity, foundational for analysing rotating machinery, gears, and satellite dish tracking, where points at different radii but the same angular speed sweep equal angles in equal time.

Interesting facts

The hour hand of a clock sweeps 360 degrees in 12 hours, meaning it moves exactly 0.5 degrees per minute -- a fact used in every clock-angle problem.

This is only half the speed of the minute hand, which moves 6 degrees per minute (360 degrees in 60 minutes), so the two hands align or separate at predictable intervals throughout the day.

Clock-angle problems are a classic application of circular motion and relative speed, and appear in aptitude tests worldwide, not just in geometry curricula.

Question details

Q15 of 56 questions

Board
CBSE
Class
Class 10
Subject
Mathematics (Standard)
Year
2026
Section
Section A
Marks
1
Type
MCQ
Chapter
Areas Related to Circles
Topic
Angle Swept by the Hour Hand of a Clock
Bloom's level
apply
Syllabus topic
Unit VI: Geometry / Mensuration — Areas Related to Circles: Sector angle and rotational speed of clock hands
Author
CBSE
Reviewed by
Padhantu Academic Team

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Frequently asked questions

Does the length of the hour hand affect the angle it sweeps?

No. The angle swept depends only on time elapsed and the hand's rotational speed (0.5° per minute for the hour hand); length only affects the arc length (distance) travelled by the tip, not the angle.

What is the angular speed of the minute hand for comparison?

The minute hand completes 360° in 60 minutes, giving a speed of 6° per minute — twelve times faster than the hour hand.