# Sphere : How Come 1/3 Ratio Applied?

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#### Danang

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##### Sphere : How Come 1/3 Ratio Applied?
« on: April 16, 2020, 02:33:35 PM »
Is it that easy to figure out the volume of a sphere by the constant 1/3 ?

It surely fit to flat base area. But a fraction of sphere by definition is a ROUND base area with certain height.
If you treat the same way between flat base area and round base area, there will be miscalculation. Because the volume will be less 1/3 base area times height.

As you know, a pyramid has multiple heights depending on where the position is. Those are the minimum height, say, h=1 to h>1 as the pointer goes to the side points.

If transforemed to be a cone it will be like this:

Still, the height has multiple sizes.

Now let's compare both objects with a fraction of a sphere:

The heights are Constant Everywhere, which means the calculation of final volume will be LESS than 1/3 ratio of base area times height.

The multiple heights of pyramid will be substracted to be the flat minimum height >> h=1 or r=1.

Pyramid's multiple heights becomes sphere's flat height AKA radius which all becomes minimum.

How come you still use the constant of 1/3 ? Isn't a fraction of rounded sphere is ensmalled version of a pyramid?

Now we work on pi, but you can prove me wrong if you have evidence.  Can you?

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#### Danang

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##### Re: Sphere : How Come 1/3 Ratio Applied?
« Reply #1 on: April 17, 2020, 04:04:33 AM »
0:51

Use your ruler. It's more than 1/3.
Even the cylinder is not full after getting poured with sphere's water.

To apply phew legacy,   i.e. Sphere Volume = (1/2 phew) ^3 × r^3

Now >> Sphere Volume = (1/2 pi) ^3 × r^3 = 3.87578 r^3.

The volume ratio of Sphere : Cylinder = 3.87578 : 6.28318 = 0.61685 : 1.
Not 0.66666 : 1
« Last Edit: April 17, 2020, 08:52:20 AM by Danang »
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#### Danang

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##### Re: Sphere : How Come 1/3 Ratio Applied?
« Reply #2 on: April 17, 2020, 08:47:09 AM »
No reply since yesterday...

case closed. 👌
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#### Danang

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##### Re: Sphere : How Come 1/3 Ratio Applied?
« Reply #3 on: April 17, 2020, 08:50:20 AM »
With just ONE PUNCH, Rabinoz, JackBlack, MicroBeta, Sokarul, CuriouserAndCuriouser got KO!!! 😅😅😅
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#### JackBlack

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##### Re: Sphere : How Come 1/3 Ratio Applied?
« Reply #4 on: April 22, 2020, 03:17:25 PM »
No reply since yesterday...

case closed. 👌
Sure, case closed.
All you have are pathetic ravings of a mad man.

How about you try to actually provide the mathematically derivation of the volume of a sphere, instead of baseless claims like "it must be less than this".
I thought I had already provided it, showing how if the area of a circle is pi*r^2 (which it is) then the volume of a sphere MUST be (4/3)*pi*r^3

#### Danang

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##### Re: Sphere : How Come 1/3 Ratio Applied?
« Reply #5 on: April 23, 2020, 02:47:48 AM »
your math should match with real experiment.
So far no experiment indicate 1/3 thing.

go to 0:40
use a ruler to measure the height of the empty space of the cylinder after it's poured with the 1st cone's water.
If you expect the empty space will be left a half after the second cone's water getting poured, you'll be wrong.

And the way the 1st and the 2nd red lines be drawn is not even. The 1st line is under the surface, the second is above the surface.

This experiment is not transparent by the way. They didn't show the entire cylinder.
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#### Danang

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##### Re: Sphere : How Come 1/3 Ratio Applied?
« Reply #6 on: April 23, 2020, 02:50:34 AM »
"Maths Without Experiment is Blind" -- Albert Einstein (2020)
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#### JackBlack

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##### Re: Sphere : How Come 1/3 Ratio Applied?
« Reply #7 on: April 23, 2020, 05:14:17 AM »
your math should match with real experiment.
We have been over this before.

With pure math, you can elliminate errors.
With real experiments, there will always be some error.

If your expected result was 0.5, and your actual result was 0.51, do they disagree? That depends upon the level of error in the experiment.
Is your observed value actually 0.51, or do the errors make it 0.49?

It is bad enough to rely upon measurements like from a ruler, but then you start pouring water around...
Have you made sure every single molecule of water was transferred? Did you make sure none evaporated?

Minor errors in experiment cannot refute the pure math.

#### Danang

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##### Re: Sphere : How Come 1/3 Ratio Applied?
« Reply #8 on: April 23, 2020, 05:34:56 PM »
Unfortunately the nature of RECTANGLE is  DIFFERENT from the nature of CURVE.
1/3 constant is related with rectangled objects.
And for the sphere volume there must be three arc constants in multiplication, i.e. anything related to pi  pi, or pi/2, or pi/4.

The three dimentions of a sphere are definitely not straight lines. Those are curved.

r=1, if a cube has the volume of 2r × 2r × 2r, a sphere will be [(pi/4)×2r] × [(pi/4)×2r] × [(pi/4)×2r] = [(pi/4)×2r]^3 = [(pi/2)×r]^3 = (pi/2)^3 × r^3

So if compared to a cube's volume which is 2^3 = 8, sphere volume is a little bit under 50%.

Goto the video

Use a ruler.
The blue water's volume/height is a bit more than 50% of the cube's volume/height.

Such (repeated) evidence confims that the sphere's volume is NOT a bit more than 50% of cube's volume.
It's a bit  less than 50% of cube's volume.
« Last Edit: April 23, 2020, 05:37:13 PM by Danang »
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#### Bullwinkle

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##### Re: Sphere : How Come 1/3 Ratio Applied?
« Reply #9 on: April 23, 2020, 05:52:06 PM »
1+1 not always 2

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#### JackBlack

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##### Re: Sphere : How Come 1/3 Ratio Applied?
« Reply #10 on: April 24, 2020, 05:05:34 AM »
1/3 constant is related with rectangled objects.
Nope. 1/3 is for any object where:
There is a line.
Perpindicular to this line at any given point there is a shape.
This shape remains similar throughout the length of the line.
This shapes changes by a constant linear scale as it moves along the line, reaching a size of 0 at one end of the line.

This produces a 3D shape known as a pyramid or cone.

For a sphere you have (4/3)*pi, i.e. the volume is (4/3)*r^3. If you compare that to a cube, with a side length of 2*r, you will have a volume of 8*r^3 for the cube. This is a ratio of pi/6, or roughly 52%.

Just because a sphere is 3D doesn't mean you have to have pi in it 3 times.

This is just like area and length. They all only have it in there 1 time.

If you want more, then try higher dimensional spheres.

Such (repeated) evidence confims that the sphere's volume is NOT a bit more than 50% of cube's volume.
It's a bit  less than 50% of cube's volume.
No, it doesn't. Firstly, you don't have repeated experiments, you have 1.
Even if you did, you are still completely ignoring any possible experiment errors involved.

You are yet to show your value contradicts known math.
In order to do so you actually need to know the experimental errors and get them low enough such that the known value lies outside.
This also includes any errors in the measurement.
The best section of the video has the cube (the relevant section of it) a mere ~155 px high, with each edge stretching across a few px.
That means each px is roughly 0.64 pp and thus each edge would be rouglhy 1.3 pp.
So when you combine 2 edges you are at an error of over 2 pp.
Far too much for you to tell the difference between 50% and pi/6.

You then have the systematic errors of the experiment (which do act against each other).
The ball must always be smaller than the cube or it wont fit. This is also seen from it wobbling. If the ball is just 4.9 cm instead of 5, your percentage drops to 0.49%, just below 50.
When you remove the ball, some water may come with it, making the ball appear larger.
Also, the ball has a mount on top which also displaces water making it larger.
You then have the question of if it is actually a cube or if it is just a rectangular prism, and if it is a sphere or an ellipsoid.

So what you actually have is an experiment with many significant limitations allowing you to see that the volume of a sphere is roughly 52%, in accordance with known math.

Meanwhile, like I said before, the pure math doesn't have this problem. It doesn't suffer from experimental error and instead provides the exact value (expressed in terms of pi) of the ratio.

#### MicroBeta

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##### Re: Sphere : How Come 1/3 Ratio Applied?
« Reply #11 on: May 09, 2020, 02:57:23 AM »
Here.  I've derived the equation for the volume of a sphere for you.  It shows where it all comes from.

It seems my original link didn't work so here is another one.

https://www.dropbox.com/s/nh2ly1g49fbgzk2/sphere.pdf?dl=0

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