



 
Hi Jane, I am not sure what measurement is 30 feet. Can you possibly sent a photo or diagram of the dome? Penny Jane responded
Thanks Jane. Unfortunately I can't give you an exact answer, the best I can to is approximate the length. Since the height at the apex is 20 feet I know that the curve is not half a circle. If it were a circle the height would be 15 feet so your Quonset is taller than it would be if the curve were a circle. I don't know what the curve is and I am going to guess that it is approximately a parabola. The diagram below of a segment of a parabola is from a page on the Wolfram MathWorld site. If my assumption that the curve of your Quonset is a parabola then $a = 15$ feet and $h = 20$ feet. The Wolfram MathWorld page gives the length, $s$ of the arc over the top of the Quonset as \[s = \sqrt{a^2 + 4 h^2} + \frac{a^2}{2 h} \sinh^{1} \left(\frac{2h}{a} \right).\] With $a = 15$ feet and $h = 20$ feet my calculations give $s = 52.3$ feet. I hope this helps,  


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