
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 8th, 2017, 01:27 PM  #1 
Senior Member Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3  calculating volume of three intersecting cylinders
Three cylinders of radius 1 intersect at right angles at the origin. Find the volume contained inside all three cylinders. Would anyone show me how to use double integral to solve this problem first with the Cartesian coordinate and then with polar coordinate? Answer: $\displaystyle 16  8 \sqrt{2} $ 
October 8th, 2017, 03:34 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,505 Thanks: 1374 
i vaguely remember doing this by taking 8 times the volume of the solid within the first octant. All 8 octants are identical. That volume would seem to then be $2\sqrt{2}$ see if you can work it that way. 

Tags 
calculating, cylinders, intersecting, volume 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Calculating three intersecting cylinders  zollen  Calculus  0  April 14th, 2017 03:54 PM 
Volume of Intersection of Two Cylinders  John Travolski  Calculus  1  April 9th, 2017 12:29 PM 
Deriving Equation for Intersecting Cylinders Surface Area  Mearntain  Calculus  3  March 15th, 2016 05:03 AM 
Calculating intersecting lines in 3D  SoulRyder  Computer Science  2  May 4th, 2014 11:37 AM 
Volume of intersection of cylinders  etidhor  Algebra  9  December 1st, 2012 08:44 AM 