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The minute hand and the hour hand of a clock are 14 cm and 7 cm long respectively. The total distance covered by their tips in one day is
- a)24 m
- b)26 m
- c)22 m
- d)none of the above
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The minute hand and the hour hand of a clock are 14 cm and 7 cm long r...
Distance Travel by hour hand in one day is = 2 � 2 πr
= 2 � 2 � (22/7) � 7 = 88 cm
Distance Travel by minute hand in one day is = 2 πr � 24
= 2 � (22/7) � 14 � 24 = 2112 cm
Total distance covered by their tips is = 2112 + 88 = 2200 cm = 22m
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= 2 � 2 � (22/7) � 7 = 88 cm
Distance Travel by minute hand in one day is = 2 πr � 24
= 2 � (22/7) � 14 � 24 = 2112 cm
Total distance covered by their tips is = 2112 + 88 = 2200 cm = 22m
Most Upvoted Answer
The minute hand and the hour hand of a clock are 14 cm and 7 cm long r...
Given:
Length of minute hand = 14 cm
Length of hour hand = 7 cm
To find:
Total distance covered by the tips of the minute hand and hour hand in one day.
Explanation:
1. The minute hand completes one full revolution in 60 minutes, which is equivalent to 12 hours. Since there are 24 hours in a day, the minute hand will complete 2 full revolutions in one day.
2. The length of the minute hand is 14 cm. Hence, the distance covered by the tip of the minute hand in one revolution is equal to the circumference of a circle with a radius of 14 cm.
Circumference of a circle = 2πr
Distance covered by the tip of the minute hand in one revolution = 2π × 14 cm
3. Similarly, the hour hand completes one full revolution in 12 hours. Since there are 24 hours in a day, the hour hand will complete 2 full revolutions in one day.
4. The length of the hour hand is 7 cm. Hence, the distance covered by the tip of the hour hand in one revolution is equal to the circumference of a circle with a radius of 7 cm.
Distance covered by the tip of the hour hand in one revolution = 2π × 7 cm
5. Therefore, the total distance covered by the tips of the minute hand and hour hand in one day is equal to:
2 revolutions of the minute hand + 2 revolutions of the hour hand
= (2 × 2π × 14 cm) + (2 × 2π × 7 cm)
= 4π × 14 cm + 4π × 7 cm
= 56π cm + 28π cm
= 84π cm
6. To find the distance in meters, we need to convert cm to meters by dividing by 100.
Total distance covered in one day = 84π cm ÷ 100
≈ 0.84π m
7. The value of π is approximately 3.14.
Total distance covered in one day ≈ 0.84 × 3.14 m
≈ 2.64 m
8. Therefore, the correct answer is option C) 22 m.
Note: The correct answer should be 2.64 m, not 22 m as stated in option C.
Length of minute hand = 14 cm
Length of hour hand = 7 cm
To find:
Total distance covered by the tips of the minute hand and hour hand in one day.
Explanation:
1. The minute hand completes one full revolution in 60 minutes, which is equivalent to 12 hours. Since there are 24 hours in a day, the minute hand will complete 2 full revolutions in one day.
2. The length of the minute hand is 14 cm. Hence, the distance covered by the tip of the minute hand in one revolution is equal to the circumference of a circle with a radius of 14 cm.
Circumference of a circle = 2πr
Distance covered by the tip of the minute hand in one revolution = 2π × 14 cm
3. Similarly, the hour hand completes one full revolution in 12 hours. Since there are 24 hours in a day, the hour hand will complete 2 full revolutions in one day.
4. The length of the hour hand is 7 cm. Hence, the distance covered by the tip of the hour hand in one revolution is equal to the circumference of a circle with a radius of 7 cm.
Distance covered by the tip of the hour hand in one revolution = 2π × 7 cm
5. Therefore, the total distance covered by the tips of the minute hand and hour hand in one day is equal to:
2 revolutions of the minute hand + 2 revolutions of the hour hand
= (2 × 2π × 14 cm) + (2 × 2π × 7 cm)
= 4π × 14 cm + 4π × 7 cm
= 56π cm + 28π cm
= 84π cm
6. To find the distance in meters, we need to convert cm to meters by dividing by 100.
Total distance covered in one day = 84π cm ÷ 100
≈ 0.84π m
7. The value of π is approximately 3.14.
Total distance covered in one day ≈ 0.84 × 3.14 m
≈ 2.64 m
8. Therefore, the correct answer is option C) 22 m.
Note: The correct answer should be 2.64 m, not 22 m as stated in option C.
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The minute hand and the hour hand of a clock are 14 cm and 7 cm long respectively. The total distance covered by their tips in one day isa) 24 m b) 26 m c) 22 m d) none of the above Correct answer is option 'C'. Can you explain this answer?
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