Question

The minute hand of a clock is 21 cm long. The distance covered by the tip of minute hand from 2:10 pm to 2:25 pm is :

• A. 346.5 cm
• B. 33 cm
• C. 66 cm
• D. 16.5 cm

Hint:

An easier way to find the fraction of the circle swept is to express the elapsed time over 60 minutes:
\[ \text{Fraction of circle} = \frac{\text{Elapsed Time}}{60} = \frac{15}{60} = \frac{1}{4} \]
Then, the distance is simply one-fourth of the total circumference:
\[ \text{Distance} = \frac{1}{4} \times 2\pi r = \frac{1}{4} \times 2 \times \frac{22}{7} \times 21 = 33\ \text{cm} \]
This eliminates the need to calculate the degree angle explicitly!

Answer 1

The Correct Option is B

Step 1: Understand what is being asked.
The minute hand is 21 cm long, and we need the distance its tip covers from 2:10 pm to 2:25 pm. Instead of finding the swept angle first, let us find the distance the tip covers in exactly one minute, then scale it up.

Step 2: Find the full circumference traced in one hour.
In 60 minutes, the tip of the minute hand completes one full circle of radius 21 cm, so it travels a distance equal to the circumference:
\[ \text{Circumference} = 2\pi r = 2\times\frac{22}{7}\times 21 = 132 \text{ cm} \]
Step 3: Find the distance covered in one minute.
Since the tip covers 132 cm uniformly over 60 minutes, the distance covered per minute is:
\[ \text{Distance per minute} = \frac{132}{60} = 2.2 \text{ cm} \]
Step 4: Scale up to the actual time elapsed.
The time from 2:10 pm to 2:25 pm is $25-10=15$ minutes, so:
\[ \text{Distance} = 15\times 2.2 = 33 \text{ cm} \]
Final Answer:
The distance covered by the tip is 33 cm, matching option (B).
\[ \boxed{33 \text{ cm}} \]