Question

a man jogging along a circular track at the speed pf 11 km per hour, traverses in 36 seconds an arc of 56 degree. find the diameter of the track in metres​

Answer 1

Answer:

The diameter of the track is approximately 222.81 metres

Step-by-step explanation:

The man covers a arc of 56 degrees in 36 seconds. So to cover 360 degrees,

$= \frac{ 360 \times 36 }{ 56 } = 231.42 \ secs$

Converting the above value to hours,

$231.42 /3600 = 0.064 \ hrs$

In 1 hr, the man covers 11 km, so in 0.064 hrs, he will cover,

$11 \times 0.064 = 0.7 \ km$

That makes approximately 700 metres. Hence, the circumference of the track is 700 metres. So the diameter is,

$circumference = \pi d\\\frac{700}{\pi} = d\\d = 222.81 \ m$

Hence, the diameter of the track is approximately 222.81 metres.

Please note that all the calculations are rounded to 2 decimal places.