How long will a man take to make a round of a circular field of radius 21 m, cycling at the speed of `8 km//h`? 

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Find the Circumference of the Circular Field
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:
- Radius \( r = 21 \) m
- We will use \( \pi \approx \frac{22}{7} \)

Substituting the values:
\[ C = 2 \times \frac{22}{7} \times 21 \]
Calculating this:
\[ C = 2 \times \frac{22 \times 21}{7} = 2 \times \frac{462}{7} = 2 \times 66 = 132 \text{ m} \]

### Step 2: Convert Speed from km/h to m/s
The speed is given as \( 8 \) km/h. To convert this to meters per second (m/s), we use the conversion factor:
\[ 1 \text{ km/h} = \frac{1000 \text{ m}}{3600 \text{ s}} = \frac{5}{18} \text{ m/s} \]
Thus, we convert \( 8 \) km/h to m/s:
\[ \text{Speed} = 8 \times \frac{5}{18} = \frac{40}{18} = \frac{20}{9} \approx 2.22 \text{ m/s} \]

### Step 3: Calculate the Time Taken to Complete One Round
We know the formula relating speed, distance, and time:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Rearranging this formula to find time gives:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the values:
\[ \text{Distance} = 132 \text{ m}, \quad \text{Speed} = 2.22 \text{ m/s} \]
\[ \text{Time} = \frac{132}{2.22} \]
Calculating this:
\[ \text{Time} \approx 59.4 \text{ seconds} \]

### Final Answer
The man will take approximately **59.4 seconds** to make a round of the circular field.

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