The total distance covered by the tips of the minute and hour hands of a clock in one day is 22 m.

To solve this problem, we need to understand the movement of the minute and hour hands of a clock and calculate the total distance covered by their tips in one complete rotation, which is equivalent to one day.

1. Movement of the Minute Hand:
- The minute hand of a clock completes one full rotation in 60 minutes (1 hour).
- In one minute, the minute hand covers 360 degrees of the clock face.
- Therefore, the minute hand covers 360 degrees in 60 minutes, which means it covers 6 degrees per minute.

2. Movement of the Hour Hand:
- The hour hand of a clock completes one full rotation in 12 hours.
- In one hour, the hour hand covers 360 degrees of the clock face.
- Therefore, the hour hand covers 360 degrees in 12 hours, which means it covers 30 degrees per hour.

3. Calculation of Total Distance Covered:
- The minute hand is 14 cm long, so in one complete rotation, it covers a circumference of 2πr = 2π(14) = 28π cm.
- The hour hand is 7 cm long, so in one complete rotation, it covers a circumference of 2πr = 2π(7) = 14π cm.
- Since the minute hand covers 360 degrees (or 2π radians) and the hour hand covers 360 degrees (or 2π radians) in one complete rotation, we can calculate the total distance covered by their tips using the formula:
Total Distance = [(Length of Minute Hand) × (Circumference covered by Minute Hand)] + [(Length of Hour Hand) × (Circumference covered by Hour Hand)]
Total Distance = (14 cm) × (28π cm) + (7 cm) × (14π cm)
Total Distance = 392π cm + 98π cm
Total Distance = 490π cm

4. Conversion to Meters:
- To convert the distance from cm to meters, we divide by 100:
Total Distance = 490π cm ÷ 100
Total Distance = 4.9π m

5. Approximation:
- To get an approximate value, we can substitute the value of π as 3.14:
Total Distance ≈ 4.9 × 3.14 m
Total Distance ≈ 15.386 m

6. Final Answer:
- Rounding off to the nearest meter, the total distance covered by the tips of the minute and hour hands in one day is approximately 15 m.

Therefore, the correct answer is option C) 22 m.