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In everyday English, "sphere" means a round object. People will think of the insides as part of the sphere.

In Mathematics it specifically means the surface of the ball.

How did the different meanings arise? Which was in use earlier and how did they end up becoming so confusing?

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    $\begingroup$ The meanings did not really "arise", the use was always ambiguous going back to ancient Greek sphaira, see etymonline. Even in mathematics today "sphere" can refer to a ball, as in "volume of a sphere". Using the same word for both a body and its boundary is not restricted to "sphere", take "triangle", "square", "cylinder", etc., see MathEd SE. This does not cause much confusion because the ambiguity is either easily resolved by context or is of little consequence (especially in everyday use). $\endgroup$
    – Conifold
    Commented Sep 1, 2022 at 0:22
  • $\begingroup$ The use of the word "ball" is very recent and finds its origin in topology . It would have sound strange to the ears of mathematicians even in the first half of the 20th century... $\endgroup$ Commented Sep 1, 2022 at 22:05

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