An athlete completes one round of a circular track of radius 10 m in 40 s . The distance covered by him in 2 min 20 s is

Options

A. 70 m
B. 140 m
C. 110 m
D. 220 m

Answer

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

### Step 1: Calculate the Circumference of the Circular Track
The distance covered in one complete round of the circular track is given by the formula for the circumference of a circle:

\[ \text{Circumference} = 2 \pi R \]

Where \( R \) is the radius of the circular track. Given that the radius \( R = 10 \, \text{m} \):

\[ \text{Circumference} = 2 \pi \times 10 = 20 \pi \, \text{m} \]

### Step 2: Convert the Time into Seconds
The total time given is 2 minutes and 20 seconds. We need to convert this into seconds:

\[ \text{Total time} = 2 \times 60 + 20 = 120 + 20 = 140 \, \text{s} \]

### Step 3: Determine the Number of Rounds Completed
The athlete completes one round in 40 seconds. To find out how many rounds he completes in 140 seconds, we divide the total time by the time taken for one round:

\[ \text{Number of rounds} = \frac{140 \, \text{s}}{40 \, \text{s/round}} = 3.5 \, \text{rounds} \]

### Step 4: Calculate the Total Distance Covered
Now, we can calculate the total distance covered by the athlete in 3.5 rounds. The distance covered is the number of rounds multiplied by the circumference of the track:

\[ \text{Total distance} = \text{Number of rounds} \times \text{Circumference} \]

Substituting the values we found:

\[ \text{Total distance} = 3.5 \times 20 \pi \]

Calculating this further:

\[ \text{Total distance} = 3.5 \times 20 \times 3.14 \approx 3.5 \times 62.8 \approx 219.8 \, \text{m} \]

Rounding this off, we find:

\[ \text{Total distance} \approx 220 \, \text{m} \]

### Final Answer
The distance covered by the athlete in 2 minutes and 20 seconds is approximately **220 meters**.

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