Setting up triple integral in cylindrical coords (looking to check my answer)

1. The problem statement, all variables and given/known data

set up an integral in cylindrical coords to compute the volume of the solid S bounded by the sphere x^2+y^2+z^2=12 and the cone 3z^2=x^2+y^2 where z>=0

3. The attempt at a solution

i will post my answer here. plz let 'I' stand for integral:

i get,

I[0,2pi] , I[0,3] I[r/sqrt[3],sqrt[12-r^2] r dz dr dtheta.

so theta goes from 0 to 2pi
r goes from 0 to 3 etc

thank you
Last edited:


Science Advisor
Homework Helper
It says to find volume. So the function you are integrating is '1'. That's a little hard to read, but it looks ok to me.

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