## anonymous 4 years ago Nina designed an arch made of wrought iron for the top of a mall entrance. The 11 segments between the two concentric semicircles are each 3 ft long. Find the total length of wrought iron used to make this structure. Round your answer to the nearest foot.

1. anonymous

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2. amistre64

well, arc length = angle * radius; angle seems to be pi and radius is 10 on one and 13 on the other

3. amistre64

then count the segments and times it by 3

4. amistre64

10pi + 13pi + 3(11) seems about right

5. anonymous

how did you get the 13?

6. amistre64

10 + 3 feet more for the space between them

7. amistre64

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8. anonymous

but why do you need both 13 pi and 10pi?

9. amistre64

you have 2 arches; one is an inner arch with a radius of 10; the other is an exterior arch with a radius of 13 and you got all these little 3 ft sections to keep them apart

10. amistre64

the total amount of material has to be the inclusion of the total length

11. anonymous

oh ok i get it know thank you!

12. amistre64

youre welcome :)