How can I find the volume of this strange body? I need to calculate the volume of a body using multiple integrals. The body's boundary is defined by a surface whose formula is 
$$0 \leq z \leq c \cdot \sin\left(\pi \sqrt{{{x^2} \over{a^2}} + {{y^2} \over{b^2}}}\right)$$
where $a$, $b$ and $c$ are some positive parameters.
The problem is that I have no idea what this body looks like. It's the first time I'm meeting sinus function in multitple integrals and it totally confuses me. I've tried to use the most popular substitutes, such as cylindrical and spherical coordinates, but it didn't help at all.
Thanks for any help!

For $a = b = c = 1$, the surface looks like this

However, the surface intersects the $z = 0$ plane

Hence, the body is not connected. The volume of each component can be computed using polar coordinates. This volume is $\infty$.
