I'm making wooden cylinders to hold appx. 200 cu in of stuff. I made
one 7.125" tall x 6 dia (id) & was going to make another 7.125" dia x
6 " tall & the tow volumes come out differently mathematically -201 cu
in vs 239 cu in-- the numbers really get wierd when using 6" tall & 4"
dia vs 4d & 6 h. Does anybody know if the latter (the 4 x 6 vs 6 x 4
example) will hold the same amount of liquid or sand?

On 2 Dec 2004 14:12:26 -0800, (Phil) wrote:

I'm making wooden cylinders to hold appx. 200 cu in of stuff. I made
one 7.125" tall x 6 dia (id) & was going to make another 7.125" dia x
6 " tall & the tow volumes come out differently mathematically -201 cu
in vs 239 cu in-- the numbers really get wierd when using 6" tall & 4"
dia vs 4d & 6 h. Does anybody know if the latter (the 4 x 6 vs 6 x 4
example) will hold the same amount of liquid or sand?

volume of a cylinder is height x area or height x pi x radius squared.

"Phil" wrote in message
om...
I'm making wooden cylinders to hold appx. 200 cu in of stuff. I made
one 7.125" tall x 6 dia (id) & was going to make another 7.125" dia x
6 " tall & the tow volumes come out differently mathematically -201 cu
in vs 239 cu in-- the numbers really get wierd when using 6" tall & 4"
dia vs 4d & 6 h. Does anybody know if the latter (the 4 x 6 vs 6 x 4
example) will hold the same amount of liquid or sand?

Simple math tells you that the one with the larger radius would hold about
50% more.
Because a cylinder has parallel sides the volume is easy to calculate. Area
of the base x height will give you the answer. (pi * r^2)*h.

301ci vs 452ci

"J" wrote in message
...

301ci vs 452ci

I think you slipped a digit in your calcs. The OP had it right : 201 vs. 239

Bob

"Bob" wrote in message
ink.net...

"J" wrote in message
...

301ci vs 452ci

I think you slipped a digit in your calcs. The OP had it right : 201 vs.
239

Bob


201 and 239 are the numbers for the 7.125x6 version.

My problem was, I forgot to convert diameter into radius. :-(
Divide by 4 and all will be well!

75 and 113

They will come out even if height and diameter are the same, but in any
other case, the version with the larger number as the diameter will be
largest (this is because in the equation it is squared.) Interestingly, the
ratio between the two versions is equal to the ratio of the two dimensions
ie: 4x6 means that the 6"d x 4"h one is 6/4ths the size of the 4"d x 6"h
one.

-j

The equation for finding the volume of cylinder is (radius times radius times PI) times the length so..
7.125 / 2 = 3.5625
3.5625 squared = 12.69140625
12.69140625 times PI = 39.8711949609375
39.8711949609375 times 6 tall = 239.227169765625 cubic inches volume
whereas
6 / 2 = 3
3 squared = 9
9 times PI = 28.27341
28.27341 times 7.125 tall = 201.45445875 cubic inch volume
as difference of 37.7727110562 cubic inches volume

Now for your question..
6 dia x 4 tall:
3x3x3.14159x4=113.09724 cubic inches
4 dia x 6 tall:
2x2x3.14159x6=75.39816 cubic inches.

R. Wink

On 2 Dec 2004 14:12:26 -0800, (Phil) wrote:

I'm making wooden cylinders to hold appx. 200 cu in of stuff. I made
one 7.125" tall x 6 dia (id) & was going to make another 7.125" dia x
6 " tall & the tow volumes come out differently mathematically -201 cu
in vs 239 cu in-- the numbers really get wierd when using 6" tall & 4"
dia vs 4d & 6 h. Does anybody know if the latter (the 4 x 6 vs 6 x 4
example) will hold the same amount of liquid or sand?

"R. Wink" wrote in message
...
The equation for finding the volume of cylinder is (radius times radius
times PI) times the length so..
7.125 / 2 = 3.5625
3.5625 squared = 12.69140625
12.69140625 times PI = 39.8711949609375
39.8711949609375 times 6 tall = 239.227169765625 cubic inches volume

Are you sure it is not 239.227169765249?

The wood may have dried out a bit while you were typing. :-)

-j "that's some micrometer you've got there"

On 2 Dec 2004 14:12:26 -0800, (Phil) vaguely
proposed a theory
.......and in reply I say!:

remove ns from my header address to reply via email

Sorry, but if you mathematically calculated the first two cylinders,
how come you can't do the last two?

I'm making wooden cylinders to hold appx. 200 cu in of stuff. I made
one 7.125" tall x 6 dia (id) & was going to make another 7.125" dia x
6 " tall & the tow volumes come out differently mathematically -201 cu
in vs 239 cu in-- the numbers really get wierd when using 6" tall & 4"
dia vs 4d & 6 h. Does anybody know if the latter (the 4 x 6 vs 6 x 4
example) will hold the same amount of liquid or sand?

To calculate the volume of a cylinder:
3.14 x radius x radius x height

note: if radius* and height are in inches,
volume will be in cubic inches.

* radius=1/2 of diameter

On 03 Dec 2004 07:35:30 GMT, Pitzikcat wrote:
To calculate the volume of a cylinder:
3.14 x radius x radius x height

note: if radius* and height are in inches,
volume will be in cubic inches.

* radius=1/2 of diameter

A cylinder need not be square. Nor need it be "upright." The only
requirement is that the sides be parallel.

The volume of any cylinder is (base area)*(Height)

For a circular cylinder, (base area) = Pi*r^2

(Pitzikcat) wrote in message ...
To calculate the volume of a cylinder:
3.14 x radius x radius x height

note: if radius* and height are in inches,
volume will be in cubic inches.

* radius=1/2 of diameter

Many thanks for all replys-- Actually, I did the calculations for both
sets of sizes. They just didn't 'SEEM' right. Before I did the math,
I assumed that just by reversing the diameter and height, the same
volume would be had. Since I'm more visual than mathematical, my
thinking was that if you had two pans (roughly cylinders with
bottoms)-- say 6 x 8 and 8 x 6, they would hold the same amount of
stuff to be cooked. Still, it's visually wierd-- I bet Math teachers
have a lot of fun with students on this issue-- and I stand
(mathematically at least) corrected
Phil

On 3 Dec 2004 09:28:22 -0800, Phil wrote:
(Pitzikcat) wrote in message
...
To calculate the volume of a cylinder:
3.14 x radius x radius x height

note: if radius* and height are in inches,
volume will be in cubic inches.

* radius=1/2 of diameter

Many thanks for all replys-- Actually, I did the calculations for both
sets of sizes. They just didn't 'SEEM' right. Before I did the math,
I assumed that just by reversing the diameter and height, the same
volume would be had. Since I'm more visual than mathematical, my
thinking was that if you had two pans (roughly cylinders with
bottoms)-- say 6 x 8 and 8 x 6, they would hold the same amount of
stuff to be cooked. Still, it's visually wierd-- I bet Math teachers
have a lot of fun with students on this issue-- and I stand
(mathematically at least) corrected
Phil

Try doing the same thing with an easier shape . . say a 6x8 square
cylinger vs an 8x6 square cylinder.

The "punchline" if you will is that the base dimension is squared and
the height is not, so volume varies by the square of base dimension but
only linearly with height.

n^2 n whenever n1

In article Ye_rd.6460$_C2.5007@trndny01, wrote:
On 03 Dec 2004 07:35:30 GMT, Pitzikcat wrote:
To calculate the volume of a cylinder:
3.14 x radius x radius x height

note: if radius* and height are in inches,
volume will be in cubic inches.

* radius=1/2 of diameter

A cylinder need not be square. Nor need it be "upright." The only
requirement is that the sides be parallel.

Not correct. By definition, the ends of a cylinder are parallel *and*
perpendicular to the surface connecting them.

--
Regards,
Doug Miller (alphageek-at-milmac-dot-com)

Get a copy of my NEW AND IMPROVED TrollFilter for NewsProxy/Nfilter
by sending email to autoresponder at filterinfo-at-milmac-dot-com
You must use your REAL email address to get a response.

"Doug Miller" wrote in message
. com...
In article Ye_rd.6460$_C2.5007@trndny01, wrote:
On 03 Dec 2004 07:35:30 GMT, Pitzikcat wrote:
To calculate the volume of a cylinder:
3.14 x radius x radius x height

note: if radius* and height are in inches,
volume will be in cubic inches.

* radius=1/2 of diameter

A cylinder need not be square. Nor need it be "upright." The only
requirement is that the sides be parallel.

Not correct. By definition, the ends of a cylinder are parallel *and*
perpendicular to the surface connecting them.

that's the definition of a right circular cylinder. there's a lot of other
types of cylinders, and that's not the general definition.

http://mathworld.wolfram.com/Cylinder.html

In its most general usage, the word "cylinder" refers to a solid bounded by
a closed generalized cylinder (a.k.a. cylindrical surface) and two parallel
planes (Kern and Bland 1948, p. 32; Harris and Stocker 1998, p. 102). A
cylinder of this sort having a polygonal base is therefore a prism
(Zwillinger 1995, p. 308). Harris and Stocker (1998, p. 103) use the term
"general cylinder" to refer to the solid bounded a closed generalized
cylinder.

As if this were not confusing enough, the term "cylinder" when used without
qualification commonly refers to the particular case of a solid of circular
cross section in which the centers of the circles all lie on a single line
(i.e., a circular cylinder). A cylinder is called a right cylinder if it is
"straight" in the sense that its cross sections lie directly on top of each
other; otherwise, the cylinder is said to be oblique. The unqualified term
"cylinder" is also commonly used to refer to a right circular cylinder
(Zwillinger 1995, p. 312)

--
Regards,
Doug Miller (alphageek-at-milmac-dot-com)

Get a copy of my NEW AND IMPROVED TrollFilter for NewsProxy/Nfilter
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In article , "Charles Spitzer" wrote:

"Doug Miller" wrote in message
.com...
In article Ye_rd.6460$_C2.5007@trndny01, wrote:
On 03 Dec 2004 07:35:30 GMT, Pitzikcat wrote:
To calculate the volume of a cylinder:
3.14 x radius x radius x height

note: if radius* and height are in inches,
volume will be in cubic inches.

* radius=1/2 of diameter

A cylinder need not be square. Nor need it be "upright." The only
requirement is that the sides be parallel.

Not correct. By definition, the ends of a cylinder are parallel *and*
perpendicular to the surface connecting them.

that's the definition of a right circular cylinder.

No, it's not. Where did I say anything about circular?


--
Regards,
Doug Miller (alphageek-at-milmac-dot-com)

Get a copy of my NEW AND IMPROVED TrollFilter for NewsProxy/Nfilter
by sending email to autoresponder at filterinfo-at-milmac-dot-com
You must use your REAL email address to get a response.

"Doug Miller" wrote in message
. com...
In article , "Charles Spitzer"
wrote:

"Doug Miller" wrote in message
y.com...
In article Ye_rd.6460$_C2.5007@trndny01, wrote:
On 03 Dec 2004 07:35:30 GMT, Pitzikcat wrote:
To calculate the volume of a cylinder:
3.14 x radius x radius x height

note: if radius* and height are in inches,
volume will be in cubic inches.

* radius=1/2 of diameter

A cylinder need not be square. Nor need it be "upright." The only
requirement is that the sides be parallel.

Not correct. By definition, the ends of a cylinder are parallel *and*
perpendicular to the surface connecting them.

that's the definition of a right circular cylinder.

No, it's not. Where did I say anything about circular?

ok, you got me. i got it from the lines just above which defined volume with
a radius, which would make it be circular. that was someone else's quote.
how about right cylinder? there's still plenty of cylinders that are not
right cylinders, and your general definition is still wrong.


--
Regards,
Doug Miller (alphageek-at-milmac-dot-com)

Get a copy of my NEW AND IMPROVED TrollFilter for NewsProxy/Nfilter
by sending email to autoresponder at filterinfo-at-milmac-dot-com
You must use your REAL email address to get a response.

On Fri, 03 Dec 2004 19:22:16 GMT, Doug Miller wrote:
In article Ye_rd.6460$_C2.5007@trndny01, wrote:
On 03 Dec 2004 07:35:30 GMT, Pitzikcat wrote:
To calculate the volume of a cylinder:
3.14 x radius x radius x height

note: if radius* and height are in inches,
volume will be in cubic inches.

* radius=1/2 of diameter

A cylinder need not be square. Nor need it be "upright." The only
requirement is that the sides be parallel.

Not correct. By definition, the ends of a cylinder are parallel *and*
perpendicular to the surface connecting them.


No, that would be a "Right Cylinger"

The formula for the volume is the same for non-right cylinders.

Take your oblique cylinder and wedge it securely against your mitre
guage. Slice off the botton square.

If your blade is infinitely thin (this is geometry, not reality) the
offcut will convert your oblique cylinder into a right cylinder of the
same volume and the same height.