When the sun depletes its current core fuel, it will become a
a. red giant
b. white dwarf
c. neutron star
d. main sequence star?

a. red giant

When the sun depletes its current core fuel, it will become a red giant.

Explanation:

The stars has different evolutionary paths according to their mass. For the case of the sun, it fuses hydrogen into helium in its core, that nuclear fusion brings, as a result, a radiation pressure that counteracts the gravitational force that goes inward as a consequence of its own mass. Hence, the star will be in hydrostatic equilibrium (spherical shape) when the two forces balanced each other.    

When the hydrogen fuel runs out, the layers of the sun will start to collapse by means of the gravity, since there is not equilibrium. However, that collapse increases the nucleus temperature which allows helium to fuse in heavier elements. The suddenly nuclear reaction expands the layers again in a violent way, which leads to the expel for the most superficial layers of the sun.

The expansion of the gas drops its temperature, which leads to the change in color for red.

Remember that if you put an iron bar in contact with fire, the color of the bar will go from red to blue as the temperature increase.            

3.2x10^7