Here is one question :
Find the volume of region bounded above by paraboloid $z = 9-x^2 -y^2$ and below by the $x -y$ plane lying outside the cylinder $ x^2+ y^2=1$
I am trying to solve this question via cylindrical coordinates:
Now I can figure out that $z$ ranges from $0$ to $9 - x^2 -y^2$ But I do not understand how can I find the range for $r$ and $\theta$, The phrase "outside the cylinder" is causing some confusion due to which I cannot find $r$ and $\theta$
Can anyone please help me here ?