The minute hand a watch is 35cm long. How for does its tip move in 18minutes? `(use pi=22/7)`

Answer

To find out how far the tip of the minute hand moves in 18 minutes, we can follow these steps:

### Step 1: Calculate the circumference of the circle traced by the minute hand.
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2 \pi r \]
where \( r \) is the radius. In this case, the radius \( r \) is the length of the minute hand, which is 35 cm.

Substituting the value of \( r \):
\[ C = 2 \pi \times 35 = 70 \pi \text{ cm} \]

### Step 2: Determine the distance moved by the minute hand in 60 minutes.
Since the minute hand completes one full rotation in 60 minutes, the distance it moves in 60 minutes is equal to the circumference:
\[ \text{Distance in 60 minutes} = 70 \pi \text{ cm} \]

### Step 3: Calculate the distance moved by the minute hand in 1 minute.
To find the distance moved in 1 minute, we divide the total distance by 60:
\[ \text{Distance in 1 minute} = \frac{70 \pi}{60} = \frac{7 \pi}{6} \text{ cm} \]

### Step 4: Calculate the distance moved in 18 minutes.
Now, we can find the distance moved in 18 minutes by multiplying the distance moved in 1 minute by 18:
\[ \text{Distance in 18 minutes} = \frac{7 \pi}{6} \times 18 \]
Calculating this gives:
\[ \text{Distance in 18 minutes} = \frac{7 \times 18 \pi}{6} = \frac{126 \pi}{6} = 21 \pi \text{ cm} \]

### Step 5: Substitute the value of \( \pi \) to find the numerical distance.
Using \( \pi = \frac{22}{7} \):
\[ \text{Distance} = 21 \pi = 21 \times \frac{22}{7} = \frac{462}{7} \text{ cm} \]
Calculating this gives:
\[ \frac{462}{7} = 66 \text{ cm} \]

### Final Answer:
The tip of the minute hand moves **66 cm** in 18 minutes.

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