The length of the curve of intersection of the cylinder $25x^2 + y^2 = 25$ and the plane $x + y + z = 5$

Asked Sep 13 '16 at 23:26

Active Sep 14 '16 at 00:05

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Find, correct to four decimal places, the length of the curve of intersection of the cylinder $25x^2 + y^2 = 25$ and the plane $x + y + z = 5$.

I have tried this problem multiple times getting the same wrong answer of $44.0992$. Any help would be great.

edited Sep 14 '16 at 00:05

Alex M.

asked Sep 13 '16 at 23:26

Connor Curry

Can you show the work you did to get this answer? – user84413 Sep 13 '16 at 23:29
x = cost, y = 5 sint, z = 5 - cost - 5sint 0 ≤ t ≤ 2. I took the derivative of that vector and found the length of that vector. Then I integrated that from 0 to 2π – Connor Curry Sep 13 '16 at 23:35
I get $\int_0^{2\pi } {\sqrt {\sin ^2 t + 25\cos ^2 t + \left( {\sin t - 5\cos t} \right)^2 } dt = 29.5463 \cdots } $ – G Cab Sep 14 '16 at 00:03
Using your method (and WolframAlpha), I got an answer of 29.5464 – user84413 Sep 14 '16 at 00:04

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