What is the term for a straight line passing from side to side through the center of a circle or sphere?

The term for a straight line that passes through the center of a circle or sphere, connecting two points on its circumference, is the diameter. The diameter is significant because it is the longest chord in a circle and divides the circle into two equal halves.

To understand this concept better, consider that any line segment connecting two points on the circumference of a circle is called a chord. However, only the chord that crosses through the center and touches both sides of the circle qualifies as the diameter. The radius, on the other hand, is defined as the distance from the center of the circle to any point on its circumference, which is always half of the diameter. A sector refers to a region of a circle that is bounded by two radii and the arc between them, which is a different concept entirely.

Therefore, the diameter is a central concept in geometry that helps define the size and shape of a circle or sphere, making it the correct answer.