The true statement about the diameter of a sphere is:
The diameter of a sphere passes through the center of the circle.
This statement accurately reflects that the diameter connects two points on the surface of the sphere and passes through its center. Here’s a brief clarification of the other statements:
- The diameter is not the shortest length on a sphere; rather, it is the longest chord of the sphere.
- The diameter is not 2.5 times the length of the radius; it is actually 2 times the radius.
- The diameter is, in fact, a specific type of chord, as it connects two points on the sphere's surface through the center.
Therefore, the correct answer is the one about the diameter passing through the center.