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August 8th, 2014, 11:27 AM   #1
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2 Cylinders Attached Perpendicular, Find Length of Second Cylinder

I have this math problem I am trying to solve. So if I have two cylinders perpendicular attached and I have both radius' (R1 and R2) and length from first cylinders radius to top of second cylinder (L1), how can I find the length of the second cylinder (L2)?


Last edited by zipaway; August 8th, 2014 at 11:56 AM.
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August 8th, 2014, 11:36 AM   #2
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Well, assuming $L_1$ goes from the center of the horizontal cylinder to the top of the vertical cylinder, then it is easy to see that $L_1-L_2=R_1$, so $L_2=L_1-R_1$. To minimize $L_2$, you would want to minimize $L_1$ and maximize $R_1$.
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August 8th, 2014, 11:56 AM   #3
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But we are given R1, R2 and L1. How would we go about finding L2?
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August 8th, 2014, 11:57 AM   #4
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I just told you. $L_2=L_1-R_1$.
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August 8th, 2014, 07:09 PM   #5
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Making the same assumption about $L_1$ we have $\displaystyle L_2=L_1-\sqrt{R_1^2-R_2^2}$
if the largest external length of the upright cylinder is to be considered.

Last edited by greg1313; August 9th, 2014 at 01:49 PM.
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