Final answer:
To determine the diameter of the lake after Rohan walks around it 15 times, divide the total distance (2517 m) by 15 to find the circumference, and then divide that result by π (approximately 3.14159) to find the diameter, which is about 53.4 meters.
Step-by-step explanation:
You have asked how to find the diameter of a lake if Rohan walks around the edge of a circular lake exactly 15 times, covering a total distance of 2517 meters.
Firstly, we calculate the circumference of the lake by dividing the total distance walked by the number of times he walked around the lake:
Total distance walked (D) = Number of laps (n) × Circumference (C)
2517 m = 15 × C
C = 2517 m / 15
C = 167.8 m (approx)
Since we know the circumference, we can find the diameter (d) using the formula for the circumference of a circle, which is C = π × d, where π is approximately 3.14159.
167.8 m = 3.14159 × d
d = 167.8 m / 3.14159
d = 53.4 m (approx)
Therefore, the diameter of the lake is approximately 53.4 meters.