# Volume of three intersecting cylinders

• Feb 6th 2010, 12:14 PM
DavidEriksson
Volume of three intersecting cylinders
Hi.
I've been asked to find the volume of the region bounded by the 3 inequalities $x^2+y^2. This is, three cylinders of radius r. Using a triple integral to find the body seems to be the 'natural way', but I can't see how to calculate
$\iiint \left[x^2+y^2

Thanks!
• Feb 6th 2010, 02:06 PM
Opalg
As a starting point, look at equation (19) on this page. The pictures between equations (17) and (18) on that page illustrate how the integral is formed.
• Feb 7th 2010, 01:27 AM
DavidEriksson
So the answer is $8(2-\sqrt{2})r^3$?