The cycling track in the diagram consists of a rectangular section and two semicircular ends.

To find the total distance covered by the cyclist, let's break down the track into parts:

1. Rectangular part (AB): The distance across the rectangle (from point A to point B) is given as 100 m.

2. Semicircular parts: The radius of each semicircle is given as 49 m. The total length of both semicircular parts will be the circumference of a full circle (since two semicircles form a complete circle). The formula for the circumference of a circle is $C = 2 \pi r$, where $r$ is the radius.

   • Circumference of one semicircle = $\frac{1}{2} \times 2 \pi r = \pi r$
   • Total length of the two semicircles = $2 \pi r = 2 \pi \times 49$

Now, we can calculate the total distance covered:

$\text{Distance} = \text{Rectangular part} + \text{Two semicircles}$ $\text{Distance} = 100 + 2 \pi \times 49$

Let's compute this distance.

math

Given values

rectangle_distance = 100 # m radius = 49 # m

Circumference of the two semicircles (full circle)

circumference = 2 * math.pi * radius

Total distance

total_distance = rectangle_distance + circumference total_distanceThe total distance covered by the cyclist is approximately 407.88 meters.

Would you like further clarification or any additional calculations? Here are some related questions you could explore:

1. What would be the distance if the radius of the semicircles were different?
2. How do the dimensions of the track affect the total distance covered?
3. What is the time it would take for the cyclist to cover this distance if the speed is known?
4. How do you calculate the area of the track?
5. If the cyclist rides along the inner edge of the track, how would the distance change?

Tip: When dealing with tracks or paths with circular sections, remember that the total length is determined by combining both the straight and curved portions.