The minutes hand of a big wall clock is 35 cm long. Taking `pi = (22)/(7)`, length of the arc. Its extremity moves in 18 seconds is :

Options

A. 11 cm
B. 1.1 cm
C. 6.6 cm
D. 6 cm

Answer

To solve the problem of finding the length of the arc that the extremity of the minute hand of a wall clock moves in 18 seconds, follow these steps:

### Step 1: Identify the radius of the clock
The length of the minute hand is given as 35 cm. This length acts as the radius (r) of the circular path traced by the minute hand.

**Hint:** Remember that the radius is the distance from the center of the circle to any point on its circumference.

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

Substituting the value of \( r = 35 \, \text{cm} \) and using \( \pi = \frac{22}{7} \):
\[ C = 2 \times \frac{22}{7} \times 35 \]

**Hint:** The circumference represents the total distance the minute hand would cover in one complete revolution.

### Step 3: Calculate the total distance covered in one revolution
Now, calculate:
\[ C = 2 \times \frac{22}{7} \times 35 = \frac{1540}{7} \, \text{cm} \]
\[ C = 220 \, \text{cm} \]

**Hint:** Ensure you simplify the fraction correctly to find the total distance.

### Step 4: Determine the time taken for one complete revolution
The minute hand completes one full revolution in 60 minutes, which is equivalent to:
\[ 60 \, \text{minutes} \times 60 \, \text{seconds/minute} = 3600 \, \text{seconds} \]

**Hint:** Remember that there are 60 seconds in a minute.

### Step 5: Calculate the distance covered in one second
To find the distance covered in one second, divide the circumference by the total seconds in one revolution:
\[ \text{Distance in 1 second} = \frac{C}{3600} = \frac{220}{3600} \, \text{cm} \]

**Hint:** This gives you the distance the minute hand travels every second.

### Step 6: Calculate the distance covered in 18 seconds
Now, multiply the distance covered in one second by 18 seconds:
\[ \text{Distance in 18 seconds} = 18 \times \frac{220}{3600} \]

**Hint:** This step will give you the total distance covered in the specified time.

### Step 7: Simplify the expression
Calculating the above expression:
\[ \text{Distance in 18 seconds} = \frac{3960}{3600} = \frac{11}{10} = 1.1 \, \text{cm} \]

**Hint:** Simplifying fractions can help in finding the final answer more easily.

### Final Answer
The length of the arc that the extremity of the minute hand moves in 18 seconds is **1.1 cm**.