The correct statement about the diameter of a sphere is:
The diameter of a sphere passes through the center of the sphere.
The other statements are either incorrect or misleading. Here’s a breakdown:
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The diameter passes through the center of the sphere: This is true. The diameter is defined as the longest chord of the sphere, which extends through its center.
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The diameter is 2.5 times the length of the radius: This is false. The diameter is actually 2 times the radius (\(d = 2r\)).
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The diameter is the shortest length on a sphere: This is false. The diameter is the longest straight line that can be drawn through a sphere.
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The diameter is not a chord: This is also false. The diameter is indeed a specific type of chord that passes through the center of the sphere.
In summary, the correct statement is that the diameter of a sphere passes through its center.