Let's evaluate each of the statements provided about the diameter of a sphere:
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The diameter is the shortest length on a sphere. - This statement is false. The diameter is the longest chord of the sphere, not the shortest.
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The diameter of a sphere passes through the center of the circle. - This statement is true. The diameter of a sphere, like that of a circle, passes through the center.
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The diameter is not a chord. - This statement is false. The diameter is a special type of chord that passes through the center of the sphere.
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The diameter is 2.5 times the length of the radius. - This statement is false. The diameter of a sphere is actually 2 times the length of the radius.
Based on this evaluation, the correct statement is:
The diameter of a sphere passes through the center of the circle.