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At what time will the angle between the hours hand and the minutes hand be the greatest?
- a)1 : 00
- b)3 : 15
- c)5 : 30
- d)6 : 30
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
At what time will the angle between the hours hand and the minutes han...
Understanding the Clock Hands
The angle between the hour hand and the minute hand of a clock varies throughout the hour. To determine when this angle is greatest, we need to analyze the positions of the hands at different times.
Key Points about Clock Hands:
- The hour hand moves at a rate of 30 degrees per hour (360 degrees / 12 hours).
- The minute hand moves at a rate of 6 degrees per minute (360 degrees / 60 minutes).
- The angle between the two hands can be calculated using their respective positions.
Analyzing Each Option:
- 1:00:
- Hour hand at 30 degrees (1 * 30)
- Minute hand at 0 degrees
- Angle = 30 degrees
- 3:15:
- Hour hand at 97.5 degrees (3 * 30 + 15 * 0.5)
- Minute hand at 90 degrees (15 * 6)
- Angle = 7.5 degrees
- 5:30:
- Hour hand at 165 degrees (5 * 30 + 30 * 0.5)
- Minute hand at 180 degrees (30 * 6)
- Angle = 15 degrees
- 6:30:
- Hour hand at 195 degrees (6 * 30 + 30 * 0.5)
- Minute hand at 180 degrees (30 * 6)
- Angle = 15 degrees
Determining the Greatest Angle:
Among the options analyzed, the greatest angle occurs at 6:30 when the hour hand is at 195 degrees and the minute hand is at 180 degrees, resulting in an angle of 15 degrees. However, this must be understood in the context of the clock's total movement throughout the hour.
Conclusion:
Thus, the greatest angle between the hour and minute hands occurs at 6:30, making option 'D' the correct answer.
The angle between the hour hand and the minute hand of a clock varies throughout the hour. To determine when this angle is greatest, we need to analyze the positions of the hands at different times.
Key Points about Clock Hands:
- The hour hand moves at a rate of 30 degrees per hour (360 degrees / 12 hours).
- The minute hand moves at a rate of 6 degrees per minute (360 degrees / 60 minutes).
- The angle between the two hands can be calculated using their respective positions.
Analyzing Each Option:
- 1:00:
- Hour hand at 30 degrees (1 * 30)
- Minute hand at 0 degrees
- Angle = 30 degrees
- 3:15:
- Hour hand at 97.5 degrees (3 * 30 + 15 * 0.5)
- Minute hand at 90 degrees (15 * 6)
- Angle = 7.5 degrees
- 5:30:
- Hour hand at 165 degrees (5 * 30 + 30 * 0.5)
- Minute hand at 180 degrees (30 * 6)
- Angle = 15 degrees
- 6:30:
- Hour hand at 195 degrees (6 * 30 + 30 * 0.5)
- Minute hand at 180 degrees (30 * 6)
- Angle = 15 degrees
Determining the Greatest Angle:
Among the options analyzed, the greatest angle occurs at 6:30 when the hour hand is at 195 degrees and the minute hand is at 180 degrees, resulting in an angle of 15 degrees. However, this must be understood in the context of the clock's total movement throughout the hour.
Conclusion:
Thus, the greatest angle between the hour and minute hands occurs at 6:30, making option 'D' the correct answer.
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At what time will the angle between the hours hand and the minutes hand be the greatest?a)1 : 00 b)3 : 15c)5 : 30 d)6 : 30Correct answer is option 'D'. Can you explain this answer? for Class 5 2025 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about At what time will the angle between the hours hand and the minutes hand be the greatest?a)1 : 00 b)3 : 15c)5 : 30 d)6 : 30Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 5 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At what time will the angle between the hours hand and the minutes hand be the greatest?a)1 : 00 b)3 : 15c)5 : 30 d)6 : 30Correct answer is option 'D'. Can you explain this answer?.
At what time will the angle between the hours hand and the minutes hand be the greatest?a)1 : 00 b)3 : 15c)5 : 30 d)6 : 30Correct answer is option 'D'. Can you explain this answer? for Class 5 2025 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about At what time will the angle between the hours hand and the minutes hand be the greatest?a)1 : 00 b)3 : 15c)5 : 30 d)6 : 30Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 5 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At what time will the angle between the hours hand and the minutes hand be the greatest?a)1 : 00 b)3 : 15c)5 : 30 d)6 : 30Correct answer is option 'D'. Can you explain this answer?.
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