We need to find the volume of a solid $D$ which is bounded by the paraboloid $z = 1-4(x^{2} + y^{2} )$ and the $xy$ plane.
I made use of the polar co-ordinates :
Taking $x = rcos\theta$ and $y= r sin\theta$ we get the following integral :
$ \int_0^{2\pi} \int_0^{\frac{1}{2}} \int_0^{1-4r^{2}}rdzdrd\theta $ ,
which gives the value $ \dfrac{\pi}{8}$ , but the solution says $ \dfrac{7\pi}{2}$ ,
I have already checked the calculations ,
Am I interpreting the problem incorrectly ? Can anyone tell ?