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. Show your work.
The picture that's included with this problem is a protractor with the bottom labeled 15 m
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To find the total length of wrought iron used to make the structure, we need to calculate the circumference of each concentric circle formed by the arch segments and then add them together.
Given that there are 11 segments between the two concentric circles, we can divide the total circumference into 11 equal parts.
First, let's find the radius of the larger circle. From the picture, we can see that the bottom of the arch is labeled as 15 m. Since the bottom represents the diameter of the circle, the radius would be half of that value.
Radius of larger circle = 15 m / 2 = 7.5 m
Now, we need to calculate the circumference of the larger circle.
Circumference of larger circle = 2 * π * radius
= 2 * 3.14 * 7.5
= 47.1 m (rounded to one decimal place)
Since there are 11 segments, each segment would cover 1/11th of the total circumference.
Length of each segment = Circumference of larger circle / 11
= 47.1 m / 11
= 4.28 m (rounded to two decimal places)
Since each segment is 1.25 m long, we can find the length of wrought iron used by multiplying the length of each segment by 1.25.
Total length of wrought iron used = Length of each segment * Number of segments
= 4.28 m * 11
= 47.08 m (rounded to two decimal places)
Therefore, the total length of wrought iron used to make the structure is approximately 47 meters.