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

The correct option is 220 m.

Step-by-step explanation:

1. Find the distance covered in one complete round:
The distance covered in one complete round of a circular track is equal to its circumference. The formula for the circumference of a circle is:
$\text{Circumference}=2\pi r$
Given the radius of the circular track, $r=10\text{m}$ and using $\pi =\frac{22}{7}$:
$\text{Distance of one round}=2\times \frac{22}{7}\times 10=\frac{440}{7}\text{m}$

2. Calculate the total time in seconds:
The total time during which the athlete runs is given as 2 minutes and 20 seconds. Converting this time into seconds:
$\text{Total time}=(2\times 60)\text{sec}+20\text{sec}=120\text{sec}+20\text{sec}=140\text{sec}$

3. Determine the number of rounds completed:
The athlete completes one round in 40 seconds. Thus, the number of rounds completed in 140 seconds is:
$\text{Number of rounds}=\frac{\text{Total time}}{\text{Time for one round}}=\frac{140}{40}=3.5\text{rounds}$

4. Calculate the total distance covered:
The total distance covered is the number of rounds multiplied by the distance of one round:
$\text{Total distance}=3.5\times \frac{440}{7}\text{m}$
Expressing 3.5 as a fraction, $3.5=\frac{7}{2}$, we get:
$\text{Total distance}=\frac{7}{2}\times \frac{440}{7}=\frac{440}{2}=220\text{m}$
Therefore, the distance covered by the athlete in 2 min 20 sec is 220 m.