45 handshakes would take place! i've attached how i figured this out (pardon the scribbles)
The distributive property is a(b + c) = ab + ac
Perhaps you mean to find the volume under

? It seems like you have to rely on calculus otherwise (in the case that you indeed mean

).
Assuming this, note that

describes the top half of a sphere with radius 8, which means the volume below this surface over the disk

is simply half the volume of the sphere. Thus the volume is