My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

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} $
zollen is offline  
October 8th, 2017, 03:34 PM   #2
Senior Member
romsek's Avatar
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.
romsek is offline  

  My Math Forum > College Math Forum > Calculus

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

Copyright © 2019 My Math Forum. All rights reserved.