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Sphere Volume.
03-31-2016, 11:29 AM
Post: #1
Sphere Volume.
Hi,
All of us know that Sphere Volume is calculate like this :

4/3(PI*R^3)

A short cut from Bill Kolb is : "240 'D-R' R^3 *",

But NASA (on his siteweb) say (PI*D^3)/6.

It is more easy and less steps, even I dont' see how go from first formulae to
NASA one ?

Gérard.
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03-31-2016, 11:56 AM
Post: #2
RE: Sphere Volume.
(03-31-2016 11:29 AM)ggauny@live.fr Wrote:  Hi,
All of us know that Sphere Volume is calculate like this :

4/3(PI*R^3)

A short cut from Bill Kolb is : "240 'D-R' R^3 *",

But NASA (on his siteweb) say (PI*D^3)/6.

It is more easy and less steps, even I dont' see how go from first formulae to
NASA one ?

PI * R * R * R * 8/6 =
PI * 2R * 2R * 2R * 1/6

Bernhard

That's one small step for a man - one giant leap for mankind.
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03-31-2016, 11:58 AM
Post: #3
RE: Sphere Volume.
Hi, Gérard,

Well, I forgot almost mt math after so much brain damage caused by good life and drinks... .)

Let me try:

V = 4/3 * PI * R^3

Also, we know that D = 2 * R; then R = D/2

If we replace R for D/2 in the initial equation, we get:
V = 4/3 * PI * (D/2)^3

which can also be written as:
V = 4/3 * PI * D^3 / 2^3

Or:
V = 4/3 * PI * D^3 / 8

Or:
V = 4/(3 * 8) * PI * D^3

Or:
V = 4/24 * PI * D^3

Or:
V = 1/6 * PI * D^3

Or:
V = (PI * D^3)/6

Jose Mesquita
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03-31-2016, 12:46 PM
Post: #4
RE: Sphere Volume.
(03-31-2016 11:29 AM)ggauny@live.fr Wrote:  4/3(PI*R^3)
(...)
But NASA (on his siteweb) say (PI*D^3)/6.

It is more easy and less steps, even I dont' see how go from first formulae to
NASA one ?

Take the first formula and replace R with D/2.
What do you get?

Dieter
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03-31-2016, 02:23 PM
Post: #5
RE: Sphere Volume.
Of course I have see the answers, but me I find :

4/3(Pi*(D/2)^3)
8/6(3*Pi*(D/6)^3)
and if I divise all by 6 I obtain :

8(3*Pi*D^3)
so it is 24*Pi*D^3 and it is false !

desolation !

Gérard.
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03-31-2016, 03:32 PM
Post: #6
RE: Sphere Volume.
when's the last time anyone had to fill a sphere with beer ??


(just askin', Wink)

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03-31-2016, 04:17 PM
Post: #7
RE: Sphere Volume.
Of course I prefer drink the beer, it is less complicated then do theses calculs !
LOL.

Gérard.
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03-31-2016, 04:34 PM
Post: #8
RE: Sphere Volume.
(03-31-2016 03:32 PM)TASP Wrote:  when's the last time anyone had to fill a sphere with beer ??


(just askin', Wink)

You have just brought a lot of past memories to my mind, from my good old times spent in Ghent (Belgium) studying computer technologies and of course, drinking the famous Kwak beer.
Not a complete sphere, but still it was great fun drinking it!

[Image: Kwak.jpg]

Jose Mesquita
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03-31-2016, 05:21 PM
Post: #9
RE: Sphere Volume.
The sphere thing is interesting from a computational standpoint, but I'm damned if I can think of a practical application. We've ruled out beer, what else is there ??

Wink

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03-31-2016, 06:55 PM
Post: #10
RE: Sphere Volume.
Yes, if we are not careful all the beer on the face, same with glass like a boot of cow-boy !

Gérard.
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03-31-2016, 07:20 PM
Post: #11
RE: Sphere Volume.
(03-31-2016 02:23 PM)ggauny@live.fr Wrote:  Of course I have see the answers, but me I find :

4/3(Pi*(D/2)^3)
8/6(3*Pi*(D/6)^3)
and if I divise all by 6 I obtain :

8(3*Pi*D^3)
so it is 24*Pi*D^3 and it is false !

You obviously forgot some basic math rules.

First of all, forget the brackets (except around d/2). All values are faktors, so there is no need to set brackets.

Then, (a/b)^n = a^n / b^n.
So...

   4/3 * pi * (d/2)^3
= 4/3 * pi * d^3 / 2^3
= 4/3 * pi * d^3 / 8
= 4/3/8 * pi * d^3
= 4/24 * pi * d^3
= pi * d^3 / 6

Dieter
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