Cylindrical Coordinates Triple Integral -- stuck in one place

[fhot112]

Homework Statement

Use cylindrical coordinates to evaluate triple integral E (sqrt(x^2+y^2)dv where E is the solid that lies within the cylinder x^2+y^2 = 9, above the plane z=0, and below the plane z=5-y

Homework Equations

The Attempt at a Solution

So i just need to know how to get the bounds for the dz and i have everything else.

triple integral dtheta bound: 0 to 2pi, dr bound 0 to 3, and not sure if the dz bound is 5-rsintheta?

 

[Orodruin]

and not sure if the dz bound is 5-rsintheta?

What is your argument for this and what makes you uncertain of your argument?

Also, for clarity, the bounds are on the coordinates themselves, not on the coordinate differentials.