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What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from 3 to 6?
- a)1/4
- b)1
- c)1/2
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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What fraction of a clockwise revolution does the hour hand of a clock ...
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What fraction of a clockwise revolution does the hour hand of a clock ...
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What fraction of a clockwise revolution does the hour hand of a clock ...
Explanation:
To determine the fraction of a clockwise revolution that the hour hand of a clock turns through when it goes from 3 to 6, we need to calculate the angle turned by the hour hand.
1. Angle covered by the hour hand in 12 hours:
- The hour hand of a clock completes a full revolution in 12 hours.
- Since there are 360 degrees in a circle, the angle covered by the hour hand in 12 hours is 360 degrees.
2. Angle covered by the hour hand in 1 hour:
- To find the angle covered by the hour hand in 1 hour, we divide the total angle (360 degrees) by 12 (since there are 12 hours on a clock).
- Therefore, the angle covered by the hour hand in 1 hour is 360/12 = 30 degrees.
3. Angle covered by the hour hand from 3 to 6:
- From 3 to 6, there are 3 hours.
- To find the angle covered by the hour hand from 3 to 6, we multiply the angle covered in 1 hour (30 degrees) by the number of hours (3).
- Therefore, the angle covered by the hour hand from 3 to 6 is 30 * 3 = 90 degrees.
4. Fraction of a clockwise revolution:
- Since there are 360 degrees in a full revolution, we need to determine the fraction of 360 degrees that 90 degrees represents.
- To find this fraction, we divide the angle covered (90 degrees) by the total angle in a full revolution (360 degrees).
- Therefore, the fraction of a clockwise revolution that the hour hand turns through from 3 to 6 is 90/360 = 1/4.
Therefore, the correct answer is option A) 1/4.
To determine the fraction of a clockwise revolution that the hour hand of a clock turns through when it goes from 3 to 6, we need to calculate the angle turned by the hour hand.
1. Angle covered by the hour hand in 12 hours:
- The hour hand of a clock completes a full revolution in 12 hours.
- Since there are 360 degrees in a circle, the angle covered by the hour hand in 12 hours is 360 degrees.
2. Angle covered by the hour hand in 1 hour:
- To find the angle covered by the hour hand in 1 hour, we divide the total angle (360 degrees) by 12 (since there are 12 hours on a clock).
- Therefore, the angle covered by the hour hand in 1 hour is 360/12 = 30 degrees.
3. Angle covered by the hour hand from 3 to 6:
- From 3 to 6, there are 3 hours.
- To find the angle covered by the hour hand from 3 to 6, we multiply the angle covered in 1 hour (30 degrees) by the number of hours (3).
- Therefore, the angle covered by the hour hand from 3 to 6 is 30 * 3 = 90 degrees.
4. Fraction of a clockwise revolution:
- Since there are 360 degrees in a full revolution, we need to determine the fraction of 360 degrees that 90 degrees represents.
- To find this fraction, we divide the angle covered (90 degrees) by the total angle in a full revolution (360 degrees).
- Therefore, the fraction of a clockwise revolution that the hour hand turns through from 3 to 6 is 90/360 = 1/4.
Therefore, the correct answer is option A) 1/4.
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