I have a question at the moment which states that S is a solid spherical shell bounded by the surface H, comprising the union of two surfaces (which are spheres) which are:
$x^{2}+y^{2}+z^{2}=1$
$x^{2}+y^{2}+z^{2}=0.5$
What on earth is the surface H? Is it the outer bound of the larger sphere? What does the union have to do with the surface?
A spherical shell is this thing. It tautologically has an "inner" and an "outer" wall, which are two non-intersecting spheres. Their union is the boundary in $\Bbb R^3$ of the shell itself.