How far does the tip of the minute hand of length 7 cm in a clock move in 30 min?

Answer

To find out how far the tip of the minute hand of length 7 cm moves in 30 minutes, we can follow these steps:

### Step 1: Understand the Movement of the Minute Hand
The minute hand moves in a circular path. The distance traveled by the tip of the minute hand in one complete revolution (which takes 60 minutes) is the circumference of the circle formed by the minute hand.

### Step 2: Calculate the Circumference of the Circle
The formula for the circumference (C) of a circle is given by:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle.

Given that the length of the minute hand (which is the radius) is 7 cm:
\[ C = 2 \pi \times 7 \]

### Step 3: Substitute the Value of \( \pi \)
Using \( \pi \approx \frac{22}{7} \):
\[ C = 2 \times \frac{22}{7} \times 7 \]

### Step 4: Simplify the Expression
The 7 in the numerator and denominator cancels out:
\[ C = 2 \times 22 = 44 \text{ cm} \]
This means the minute hand travels 44 cm in one complete revolution (60 minutes).

### Step 5: Calculate the Distance Traveled in 30 Minutes
Since the minute hand completes one full revolution in 60 minutes, in 30 minutes (which is half of 60 minutes), it will travel half the circumference:
\[ \text{Distance in 30 minutes} = \frac{C}{2} = \frac{44}{2} = 22 \text{ cm} \]

### Conclusion
The tip of the minute hand moves **22 cm** in 30 minutes.

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