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Suppose that, in my experiments, I have a number of cubes and a number of spheres. The volumes of cubes and spheres are not fixed. Now, I want to express this feature. I do know that the sentence

The volume of cubes is not fixed.

is correct. Because here I specify the VOLUME of cubes.

But If I want to say the volume of cubes and the volume of spheres at the same time, which one is correct?

Volumes of cubes and spheres are not fixed.

or

The volumes of cubes and spheres are not fixed.

I have such a question because I am unsure that the word 'volumes' should be general or specific here. It looks like both are correct.

I think that 'volumes' is general, because there are two kinds of volumes, I do not intend to specify which one.

I think that 'volumes' could also be specific, because the use of 'volumes' is meant to specify the two objects' volumes, not other things' volumes.

Am I correct?

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  • 1
    Please indicate why you believe that your friend might be correct. What did your research reveal about this issue? Commented Dec 12, 2022 at 3:19
  • @MarcInManhattan I update the question. Please take a look. Commented Dec 12, 2022 at 6:43
  • Your proposed sentences would read much better with a second preposition: (The) volumes of cubes and of spheres are not fixed. Commented Dec 12, 2022 at 13:14
  • @PeterShor If I have more objects, then I have to use more than two 'of'. e.g., (The) volumes of cubes, of spheres and of ellipsoids are not fixed. Is this correct? Commented Dec 13, 2022 at 6:33
  • 1
    You can use as many "of"s as you want ... there's no grammatical upper limit. Commented Dec 13, 2022 at 11:57

1 Answer 1

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Since you are talking about a specific group of cubes and spheres, rather than the geometric shapes or the class of similar objects in general, you would say "the cubes and spheres."

Since you are thereby discussing the volumes of a specific group of entities, "the volumes" would make the most sense.

So you would say:

The volumes of the cubes and spheres are not fixed.

Of course, there are a large number of exceptions to the rules around definite articles and determiners more broadly, but I'm not aware of any that apply here.

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