Jason designed an arch made of wrought iron for the top of a mall entrance. The 11 segments between the two concentric circles are each 1.25 m long. Find the total length of wrought iron used to make the structure. Round the answer to the nearest meter.

15m

59 m

Yas

To find the total length of wrought iron used to make the structure, we need to calculate the circumference of both concentric circles and add the lengths of the 11 segments.

Let's first calculate the circumference of the inner circle. The inner circle represents the bottom part of the arch, so it has a smaller radius. To find the circumference of a circle, we use the formula:

Circumference = 2 * π * radius

The 11 segments are each 1.25 meters long, so they contribute a total length of 11 * 1.25 = 13.75 meters.

Since we know the length of each segment, we can calculate the radius of the inner circle by multiplying the segment length by 11 and then dividing by 2π (since the circumference is equal to the sum of all the segment lengths).

Radius_inner = (Total length of segments) / (2 * π)
Radius_inner = 13.75 / (2 * π)
Radius_inner ≈ 2.187 meters

Now that we have the radius of the inner circle, we can calculate its circumference:

Circumference_inner = 2 * π * Radius_inner
Circumference_inner ≈ 2 * 3.14 * 2.187
Circumference_inner ≈ 13.71 meters

Next, we need to calculate the circumference of the outer circle. Since the outer circle represents the top part of the arch, it has a larger radius. We know that the outer circle has the same number of segments as the inner circle (11), so the length of each segment remains the same (1.25 meters).

Using the same formula:

Radius_outer = (Total length of segments) / (2 * π)
Radius_outer = 13.75 / (2 * π)
Radius_outer ≈ 2.187 meters

Now we can calculate the circumference of the outer circle:

Circumference_outer = 2 * π * Radius_outer
Circumference_outer ≈ 2 * 3.14 * 2.187
Circumference_outer ≈ 13.71 meters

Finally, we can calculate the total length of wrought iron used by adding the circumferences of the inner and outer circles, and the lengths of the 11 segments:

Total length = Circumference_inner + Circumference_outer + Total length of segments
Total length ≈ 13.71 + 13.71 + 13.75
Total length ≈ 41.17 meters

Rounding to the nearest meter, the total length of wrought iron used to make the structure is approximately 41 meters.