Could someone help me find the volume between these 2 paraboloids

http://i.imgur.com/4xPcOhc.png

I'm guessing you use triple integrals for this one, but I'm not entirely sure...

Use cylindrical coordinates.
z = 9(x^2 + y^2) ==> z = 9r^2.
z = 32 - 9(x^2 + y^2) ==> z = 32 - 9r^2.

These surfaces intersect when 9r^2 = 32 - 9r^2 ==> r = 4/3, a circle.

So, the volume ∫∫∫ 1 dV equals
∫(θ = 0 to 2π) ∫(r = 0 to 4/3) ∫(z = 9r^2 to 32 - 9r^2) 1 * (r dz dr dθ)
= 2π ∫(r = 0 to 4/3) r [(32 - 9r^2) - 9r^2] dr
= π ∫(r = 0 to 4/3) (64r - 36r^3) dr
= π(32r^2 - 9r^4) {for r = 0 to 4/3}
= 256π/9.

I hope this helps!