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.
and there's a picture of a arch with the measurements of 15 m
The total length of wrought iron used to make the arch can be calculated by finding the circumference of each of the concentric circles and adding the length of the 11 segments.
To find the circumference of a circle, we use the formula C = 2πr, where C is the circumference and r is the radius.
Given that the diameter (or twice the radius) of the larger circle is 15 m, the radius is 15 m / 2 = 7.5 m.
The circumference of the larger circle is C1 = 2π(7.5) = 15π m.
Similarly, the diameter of the smaller circle can be found by subtracting the length of one segment (1.25 m) from the diameter of the larger circle. The diameter of the smaller circle is 15 m - 1.25 m = 13.75 m. Thus, the radius of the smaller circle is 13.75 m / 2 = 6.875 m.
The circumference of the smaller circle is C2 = 2π(6.875) = 13.75π m.
The total length of the 11 segments is 11 segments × 1.25 m/segment = 13.75 m.
Therefore, the total length of wrought iron used to make the arch is C1 + C2 + 13.75 m = 15π + 13.75π + 13.75 m.
To approximate the answer to the nearest meter, we can calculate the numerical value of the expression:
15π + 13.75π + 13.75 ≈ 47.12 m.
Rounding this to the nearest meter, the total length of wrought iron used to make the structure is approximately 47 meters.
To find the total length of wrought iron used to make the structure, we first need to calculate the length of the 11 segments between the two concentric circles.
Given that each segment has a length of 1.25 m, we can multiply this length by the number of segments to get the total length of the 11 segments:
Total length of the segments = 1.25 m/segment * 11 segments = 13.75 m.
Next, we need to calculate the length of the circle formed by the outer edge of the arch. Since we have the diameter of the outer circle, we can use the formula for the circumference of a circle:
Circumference = π * Diameter.
Given that the diameter of the outer circle is 15 m, we can calculate its circumference:
Circumference = 3.14 * 15 m ≈ 47.1 m.
Finally, we add the total length of the segments to the circumference of the outer circle to get the total length of wrought iron used:
Total length = Total length of the segments + Circumference of the outer circle
Total length = 13.75 m + 47.1 m ≈ 60.85 m.
Rounded to the nearest meter, the total length of wrought iron used to make the structure is approximately 61 meters.