nina designed an arch made of wrought iron for the top of a mall entrance. the 11 segmentsbetween the two concentric semicircles are each 3 ft long. find the total length of the wrought iron used to make this structure. round your answer to the nearest foot
To find the total length of the wrought iron used to make the arch, we need to calculate the circumference of each semicircle and add it to the length of the 11 segments.
First, let's find the circumference of a semicircle. The formula for the circumference of a full circle is C = 2πr, where C is the circumference and r is the radius. Since we have a semicircle, we need to divide the circumference by 2.
Given that each segment is 3 ft long, we can determine the radius of the semicircle by dividing the segment length by π. Let's calculate it:
Radius = Segment Length / π
= 3 ft / π
≈ 0.9551 ft
Now, let's find the circumference of each semicircle:
Circumference of Semicircle = (2π * Radius) / 2
= π * Radius
Circumference of Semicircle ≈ π * 0.9551 ft
To find the total length of the wrought iron used, we need to multiply the circumference of the semicircle by 2 (for the two semicircles) and add the length of the 11 segments:
Total Length = (2 * Circumference of Semicircle) + (Number of Segments * Segment Length)
= (2 * π * 0.9551 ft) + (11 * 3 ft)
Calculating this expression will give us the total length of the wrought iron used for the arch. Rounding the answer to the nearest foot will provide the final result.