Final answer:
The darkest and coolest part of a sunspot is known as the umbra. It is surrounded by a less dark region called the penumbra and appears on the Sun's photosphere.
Step-by-step explanation:
The central region of a sunspot, which is its darkest and coolest part, is known as the umbra. Sunspots are observable on the Sun's photosphere, the visible surface of the Sun, where they appear as dark spots due to their cooler temperatures compared to the surrounding plasma. The temperature at the center of a large sunspot is typically about 3800 K, which is significantly lower than the average temperature of the photosphere, which is about 5800 K. Surrounding the umbra is the slightly lighter and warmer penumbra.
For further context, the chromosphere is the part of the Sun's atmosphere that lies above the photosphere, characterized by its reddish glow during solar eclipses. The corona, meanwhile, is the outermost part of the Sun's atmosphere and is best observed during total solar eclipses. However, the correct answer to the student's question is a) Umbra.