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# Confused about wording of question watch

1. I'm slightly confused about the wording of the following question:
A tetrahedron has vertices O,A,B,C. Find the centre of volume, defined by

I am confused by the s. Can anyone help me to understand the question?
Thanks,
D.
2. It means you need to integrate over the whole volume of the tetrahedron, which typically means splitting dV into dxdydz, and doing a triple integral between limits that you need to work out which will result in you integrating the full volume. The V in the fraction at the start is just the volume itself. It might be easier to start with the volume alone:

This is the hardest bit as you need to work out an appropriate set of limits
3. Yeah, I've already computed the volume. I'm confused about the notation, and the fact that we have V for both the volume and the tetrahedron, if that makes sense.
4. Ok, well yeah maybe they could have given the tetrahedron a different name but I guess they just thought it would be clear from the context of the question. It's just that V means the volume of the tetrahedron, so writing it out in full, you're looking to calculate:

which as I say was the hardest bit, so now you've got the limits to plug into the other integral:

5. (Original post by Dialetheism)
Yeah, I've already computed the volume. I'm confused about the notation, and the fact that we have V for both the volume and the tetrahedron, if that makes sense.
Yes, this question's notation is ******* awful - I've commented on this in the past.

The first V means "the volume of the tetrahedron", the second means "the tetrahedron", and the third is dV = dx dy dz. So, writing it out in better notation, you are looking to find , where T is the tetrahedron and |T| is its volume, .

Edit: snap.
6. Cheers guys, that helped.
D.

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