A question about volume (caution: Mathematics and physics question)?

 Ok, I know how to figure the "volume of a sphere" and the surface area of said sphere,  now I need to know how to figure how much I need to remove from the outside, to reduce the volume by about 1/2.  

I suspect this will NOT reduce the size of the entire sphere by 1/2....at least, that doesn't seem logical to me.

Can anyone explain it so that I (not a mathematician) can understand it?


 

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CameronSS6 years ago
Volume is a cubic function, area is a square function, distance is a linear function. If you double the area (linear), the surface area (square) will be quadrupled (22=4) and the volume (cubic) will be octupled, if that's even a word (23=8).
 
To determine linear proportions from volume, work backwards. To make the volume 1/8 of what it was, the diameter must be halved (cube root of 1/8 is 1/2). To make the volume half of what it was, the volume must be the cube root of 1/2 of the original, about 0.79. So if you start with a sphere of diameter 1", a sphere with diameter .79' will have about half the radius.

The same concept is true for all three-dimensional objects, regardless of shapes.
Goodhart (author)  CameronSS6 years ago
Ok, thanks.....let me see if I can plug that into what I am working on (the numbers are a bit on the large size, on the order of 1,409,147,148,464,966,056.25 CKm, etc. as the volume)....
You know, we already have gravity holding us in place, you don't need to put Gorilla Glue on the sun to win the contest...
Goodhart (author)  CameronSS6 years ago
Nothing like that.....I have heard someone say that the sun would have to be "double" the size it is now, if it has already used 1/2 of it's fuel, at the very beginning. Now, right away I gave him the ole o_0 look and said I'd get back to him on that (I couldn't do this in my head, and some of it I was unfamiliar with).

Now, I know my figuring will have a "grave error" in it. but it will be to his advantage and I suspect that it will STILL not come even close to what this innumerate, supposed mathematician has come up with. LOGIC tells me he's wrong, without even doing the math.
Yep, flawed logic. He's going off the (incorrect) assumption that as the sun "consumes" fuel, it disappears and does not contribute to the total volume. It's nuclear fusion, which does convert mass into energy, but only a small fraction of the mass. And it would only have to start off with about a 25% larger diameter if his method was correct.

Kelsey probably knows a better answer, but he's slacking off on the forum-answering, apparently. Probably off creating a black hole to eat the solar system or something.
Goodhart (author)  CameronSS6 years ago
Yes, but even if we assume a reduction of 1/2 over the last, what, 5 X1011 years, we STILL don't get a sun that is doubled in size that would consume (another flawed bit of logic) the planets out to Mars.  

Oooo, in a way I hate pseudo-science, and in a way I like it....it keeps me thinking.... ;-)    I have to work from scratch though....not having a heavily mathematical background....I have to figure it out as I go along. 


So,  I came up with....if 1/2 the volume of mass were removed we'd get a surface area reduction from 6,078,428,661,500 CKM  down to 4,801,958,642,585 CKm   So, even given his false information, the math still doesn't support his determination.
I think you mean 4.6 x 10^9. The whole Universe is only 13.9 x 10^9 years old.
We're talking Universe 2.0.
Goodhart (author)  CameronSS6 years ago
On the other side of the "great expanse"
Goodhart (author)  kelseymh6 years ago
Um, yeah, I am still having a few problems with converting to the short hand.... 10 9  = 10,000,000,000  right ?
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