Volume of a quarter cylinder between 2 planes

[Matternot]

Homework Statement

Find the volume V of the region that lies inside the quarter cylinder
0 ≤ r ≤ 1, 0 ≤ θ ⇐ 1/2 π and between the planes x+y+z=4 and z=0, where (r, θ, z) are cylindrical polar coordinates.

Homework Equations

integral dV = integral r drdθdz

The Attempt at a Solution

I considered 4pi (volume of cylinder up to z=4) and the volume between the planes z=0 and x+y+z = 0

My biggest problem is working out which I should take as my final variable to integrate. I assume it'll be r

 

[Matternot]

Oops... Came up with a solution leading to the result π-2/3 immediately after posting. If anyone wants to check my answer, be my guest.

 

[haruspex]

Oops... Came up with a solution leading to the result π-2/3 immediately after posting. If anyone wants to check my answer, be my guest.

Looks right.

 

[Matternot]

Looks right.

Thanks