Which dwarf planet orbits the sun in 310 years at a distance between 38.5 to 53 AU?

The correct option is Makemake.

Let us analyze the orbital characteristics of the given dwarf planets:

1. Makemake: It is a dwarf planet located in the Kuiper belt. Its distance from the Sun ranges from approximately 38.5 AU at perihelion to 52.8 AU (around 53 AU) at aphelion, and its orbital period around the Sun is approximately 309.8 years (about 310 years).

2. Pluto: Orbits the Sun at a distance ranging from 29.7 to 49.3 AU with an orbital period of about 248 years.

3. Eris: Orbits the Sun at a distance ranging from 37.8 to 97.5 AU with an orbital period of about 558 years.

4. Ceres: Located in the main asteroid belt, it orbits the Sun at a distance of 2.5 to 3.0 AU with an orbital period of about 4.6 years.

Therefore, the dwarf planet that orbits the Sun in 310 years at a distance between 38.5 to 53 AU is Makemake.