The problem is spherically symmetric so no problems with using the usual force law for gravitation:

where M is the mass of the sphere and m is the mass of the object.

To evaluate this we need the mass of the whole sphere. It has a constant mass density, call it . Then we know that

So

Now your turn. Find the mass of the removed section. Notice that the problem is still spherically symmetric so that

where is the removed mass.

Now form the fraction and you will find that practically everything cancels out.

-Dan