Find The Volume; Triple Integrals

[withthemotive]

Find the volume of the solid enclosed by the paraboloids z = (x^2 + y^2 ) and z = 32 − ( x^2 + y^2) .To make this problem easier to look at I resorting to making it into cylindrical coordinates.
{r, theta, z| 0< r< 1, 0<theta<2pi, r< z< 32-r}

Every time I solve for this I end up getting 31pi and I'm being told it's constantly wrong.

 

[tiny-tim]

Welcome to PF!

Find the volume of the solid enclosed by the paraboloids z = (x^2 + y^2 ) and z = 32 − ( x^2 + y^2) .
…
0< r< 1

Hi withthemotive! Welcome to PF!

No, r goes from 0 to … ?

(but isn't it easier just to take horizontal slices of thickness dz, and just integrate once, over z?)

 

[withthemotive]

Hi withthemotive! Welcome to PF!

No, r goes from 0 to … ?

(but isn't it easier just to take horizontal slices of thickness dz, and just integrate once, over z?)

LOL...oops.
I was looking at a similar problem on here, I think I might have figured it out now.