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A circle is just the line which is apart from the centre by a constant value so does a line have area?

And my second question is does a cube occupy a volume?

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    $\begingroup$ Technically a circle together with its interior should be called a disk, but it is common usage to call it a circle. $\endgroup$ Commented Oct 30, 2015 at 20:15
  • $\begingroup$ @WillJagy It's just my way of expressing my question but I'm not surely asking a trivial question, if you can rephrase the question please do $\endgroup$
    – user37421
    Commented Oct 30, 2015 at 21:34

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You need to distinguish between the perimeter of the circle, which is a curve without area (one can also consider it to have area $0$), and the disc enclosed by the circle, which has area $\pi r^2$.

In everyday language, the word "circle" is used for both of these concepts, and one can usually guess from context which of them is meant.

In careful mathematical language, "circle" usually tends to mean only the perimeter curve, and the disc is called a disc, but there are some traditional exceptions where even mathematicians say "circle" about the disc. In particular, speaking about the area of geometrical figures ("area of the circle", "squaring the circle", etc) is such a common exception.


For cubes not even mathematics has a well-established convention that provides different words for the solid and its surface. Both are called "cube", and it is up to the speaker to provide enough context to make it clear whether he means the polyhedral surface or also its interior.

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  • $\begingroup$ What about the cube, does it have volume? $\endgroup$
    – user37421
    Commented Oct 30, 2015 at 20:20
  • $\begingroup$ I think it's more convenient to think about a cube as a shape not an abject $\endgroup$
    – user37421
    Commented Oct 30, 2015 at 20:23
  • $\begingroup$ @AhmedElsawy As per Henning's answer, what do you mean by "cube?" (And what do you mean "a shape not an [o]bject"?) $\endgroup$ Commented Oct 30, 2015 at 20:47
  • $\begingroup$ @NoahSchweber I thought that people in the past might not have thought about geometric space and they called a cube according to its overall shape so it's not important if you refer to it as a non hollow object or a hollow one because a cube just refers to fixed way of organizing its parts, I was asking about opinions about that but in a brief comment $\endgroup$
    – user37421
    Commented Oct 30, 2015 at 20:54
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    $\begingroup$ @AhmedElsawy Purely convention. Technical terms are introduced as needed. All the variants on the circle - the circle without interior ("circle"), the circle with interior ("disc"), and just the interior of the circle ("open disc") - are incredibly useful, and come up all the time in math, so it became important to have consistent names for them. The cube, for whatever reason, not so much. $\endgroup$ Commented Oct 31, 2015 at 4:08

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