At any given time, ______ of the earth is illuminated by the sun.

The correct answer is: C. One-half

The Earth is a sphere, and the Sun is a point source of light. This means that at any given time, half of the Earth is facing the Sun and half of the Earth is facing away from the Sun. The side of the Earth that is facing the Sun is illuminated, and the side of the Earth that is facing away from the Sun is in darkness.

Option A: One-fourth is incorrect because it is not half of the Earth.
Option B: One-third is incorrect because it is not half of the Earth.
Option D: Two-thirds is incorrect because it is more than half of the Earth.