- #1
FeDeX_LaTeX
Gold Member
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Homework Statement
Find the volume of the region common to the intersecting cylinders ##x^2 + y^2 = a^2## and ##x^2 + z^2 = a^2##.
The Attempt at a Solution
I am totally stuck here. What do they mean when they say 'intersecting cylinders'? I've drawn graphs of circles of radius a, centred at the origin, in the x-y plane and the x-z plane. I've put them together and ended up with two identical circles cutting each other at right angles, and I don't see any cylinders... can anyone help me visualise this?
They have ended up with
[tex]8 \int_{x=0}^{a} \int_{y=0}^{\sqrt{a^2 - x^2}} z dy dx[/tex]
I can understand where the limits of integration come from, but not the factor of 8, nor what is actually going on here...