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: Understanding the Question:
The minute hand of a clock acts as the radius of a circle, with length \(r = 21\) cm. We need to find the distance covered by its tip as it moves from 2:10 pm to 2:25 pm. The distance covered by the tip is equivalent to the arc length of the sector swept by the hand.

Step 2: Key Formula or Approach:
1. The angle swept by a minute hand in 60 minutes is \(360^\circ\). Thus, the angle swept per minute is:
\[ \text{Angle per minute} = \frac{360^\circ}{60} = 6^\circ \]
2. Calculate the time elapsed and the corresponding angle \(\theta\) in degrees.
3. The distance covered by the tip is the arc length of the sector:
\[ \text{Arc Length } (l) = \frac{\theta}{360^\circ} \times 2\pi r \]

Step 3: Detailed Explanation:
1. Find the time elapsed between 2:10 pm and 2:25 pm:
\[ \text{Time elapsed} = 25\ \text{minutes} - 10\ \text{minutes} = 15\ \text{minutes} \]
2. Determine the central angle \(\theta\) swept by the minute hand in 15 minutes:
Since the hand sweeps \(6^\circ\) in one minute:
\[ \theta = 15 \times 6^\circ = 90^\circ \]
3. Calculate the distance covered (arc length) with \(r = 21\) cm and \(\pi = \frac{22}{7}\):
\[ l = \frac{90^\circ}{360^\circ} \times 2 \times \frac{22}{7} \times 21 \]
4. Simplify the fractions:
\[ \frac{90^\circ}{360^\circ} = \frac{1}{4} \]
\[ \frac{21}{7} = 3 \]
Substitute these back:
\[ l = \frac{1}{4} \times 2 \times 22 \times 3 \]
\[ l = \frac{1}{4} \times 132 \]
\[ l = 33\ \text{cm} \]
Hence, the tip of the minute hand covers a distance of 33 cm.

Step 4: Final Answer:
The distance covered by the tip is 33 cm, which corresponds to option (B).