My Math Forum 2 Cylinders Attached Perpendicular, Find Length of Second Cylinder

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 August 8th, 2014, 11:27 AM #1 Newbie   Joined: Aug 2014 From: canada Posts: 2 Thanks: 0 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.
 August 8th, 2014, 11:36 AM #2 Senior Member   Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53 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 $R_1$.
 August 8th, 2014, 11:56 AM #3 Newbie   Joined: Aug 2014 From: canada Posts: 2 Thanks: 0 But we are given R1, R2 and L1. How would we go about finding L2?
 August 8th, 2014, 11:57 AM #4 Senior Member   Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53 I just told you. $L_2=L_1-R_1$.
 August 8th, 2014, 07:09 PM #5 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond 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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