Describe the solid by inequalities in cylindrical coordinates which is enclosed by $\displaystyle z=0, z=x+y+1$ and the two cylinders $\displaystyle x^2+y^2=4, x^2+y^2=9 $

Just need someone to quickly verify this,

I have

$\displaystyle 2 \leq r \leq 3 $,

$\displaystyle 0 \leq \theta \leq 2\pi $ and

$\displaystyle 0 \leq z \leq x+y+1 $ (not sure how else to state that one)

is this correct?