Viviani, is it you? - hard

Let S be a sphere and C be a cylinder which are defined as follows:

$S=$ $\{$ $(x,y,z)$ $\in$ $R^{3}$ $|$ $x^{2}+y^{2}+z^{2}$ $\leq 4$ $\}$

$C=$ $\{$ $(x,y,z)$ $\in$ $R^{3}$ $|$ $(x-1)^{2}+y^{2}$ $\leq 1$ $\}$

If a,b,c are the numerical values of: the sphere surface inside the cylinder, the cylinder surface inside the sphere and the volume of the intersecting solid, respectively.

Calculate a+b+c . Round your answer to 3 significant digits