Are you sure you have written that correctly? For (x,y) close to the boundary of that disk, will be close to 36 which will make negative.

I am going to assume the function you want to integrate is . With that, since the problem says "using geometry", we can interpret this integral as the volume of a the upper half of a sphere of radius 6: gives so . Of course, on the xy-plane, z= 0 so we have , the given circle. The volume of a sphere is so the volume of the hemisphere is , which is, indeed, .

It's very easy to do that in polar coordinates: . Let and it becomes