The question is, find the volume of a region bounded by the paraboloid $z=1-4(x^2+y^2)$ and the $xy$-plane.
I have tried this question using the cylindrical coordinates and my answer comes out to be $\pi/8$ but that is incorrect the answer should come out to be $7\pi/12$.
I took the limits for $z$ from $0$ to $1-4r^2$, for $r$ from $0$ to $1/2$ and for $\theta$ from $0$ to $2\pi$.
Wonder where I went wrong. Help will be highly appreciated. I have checked the integration part that is correct, i think that the problem lies somewhere in taking the limits.