. A neutral conducting sphere contains a spherical cavity. A point charge +q is located at the |center of the cavity.

Question

A. What is the total surface charge on the interior surface of the conductor?

B. What is the total charge on the exterior surface of the conductor?

Answer 1

A. -q

B. q

Both follow from Gauss' law. Consider a spherical surface inside the metal between the interior and exterior surface (for A.). There can be no E-field flux through that surface, so the total charge inside must be zero.
Outside the sphere (for B.), the net flux is due to the charge at the center, because the surface charges on the inside and exterior of the sphere cancel.