How to solve gravitational force exerted

[Another]

problem 3.8 Classical mechanics R.Douglas Gregory
A narrow Hole is drilled through the centre of a uniform sphere of mass M and radius a . Find the gravitational force exerted on a particle of mass m which is inside the hole at a distance r from the centreF = GMm/r²(i) interior to a uniform hollow sphere with inner radius r and outer radius a
resultant force = 0
(ii) exterior to a uniform solid sphere of radius r and mass (r/a)^3 M

F = F(ii) + F(i)
F =( GMm(r/a)³ )/r² + 0
F = (GMm/a³)r ; this is answer

I don't understand F(ii) why equal ( GMm(r/a)³ )/r²

I think that F = GM(pdv)/r² how to solve ?

 

[TSny]

(ii) exterior to a uniform solid sphere of radius r and mass (r/a)^3 M
F =( GMm(r/a)³ )/r² + 0
F = (GMm/a³)r ; this is answer

What does m stand for? Is it the same as M?

[Edit: Never mind, you defined m in the problem statement. Sorry. Yes, that looks good.]

I think that F = GM(pdv)/r² how to solve ?

What do the symbols p and dv represent? Can you explain your reasoning for setting up this equation? Should the mass m appear somewhere here?