The minute hand of a clock is 21 cm long. Calculate the area swept by it and the distance travelled by tip in 20 minutes.

Answer

To solve the problem, we need to calculate two things: the area swept by the minute hand and the distance traveled by the tip of the minute hand in 20 minutes.

### Step-by-Step Solution:

**Step 1: Understand the Problem**
- The minute hand of a clock is 21 cm long. This length represents the radius (r) of the circular path traced by the minute hand.

**Step 2: Calculate the Angle Covered in 20 Minutes**
- The minute hand completes a full circle (360 degrees) in 60 minutes.
- Therefore, the angle covered in 1 minute is:
\[ \text{Angle per minute} = \frac{360 \text{ degrees}}{60 \text{ minutes}} = 6 \text{ degrees} \]
- In 20 minutes, the angle covered is:
\[ \text{Angle in 20 minutes} = 20 \text{ minutes} \times 6 \text{ degrees/minute} = 120 \text{ degrees} \]

**Step 3: Calculate the Area Swept by the Minute Hand**
- The area \(A\) swept by the minute hand can be calculated using the formula:
\[ A = \frac{\theta}{360} \times \pi r^2 \]
where \(\theta\) is the angle in degrees and \(r\) is the radius.
- Substituting the values:
- \(\theta = 120\) degrees
- \(r = 21\) cm
- \(\pi \approx \frac{22}{7}\)

The area calculation becomes:
\[ A = \frac{120}{360} \times \frac{22}{7} \times (21)^2 \]
\[ A = \frac{1}{3} \times \frac{22}{7} \times 441 \]
\[ A = \frac{22 \times 441}{21} \quad (\text{since } 3 \times 7 = 21) \]
\[ A = \frac{9702}{21} = 462 \text{ cm}^2 \]

**Step 4: Calculate the Distance Travelled by the Tip of the Minute Hand**
- The distance \(D\) traveled by the tip of the minute hand can be calculated using the formula:
\[ D = \frac{\theta}{360} \times 2\pi r \]
- Substituting the values:
\[ D = \frac{120}{360} \times 2 \times \frac{22}{7} \times 21 \]
\[ D = \frac{1}{3} \times 2 \times \frac{22}{7} \times 21 \]
\[ D = \frac{44}{7} \times 21 \times \frac{1}{3} \]
\[ D = \frac{924}{7} = 132 \text{ cm} \]

### Final Answers:
- Area swept by the minute hand: **462 cm²**
- Distance traveled by the tip in 20 minutes: **132 cm**