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.
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
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 113They 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 volumeNow 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. W>I'm making wooden cylinders to hold appx. 200 cu in of stuff. I made
times PI) times the length so..
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, snipped-for-privacy@yahoo.com (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?
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.
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
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 n>1
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)
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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.
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)
No, it's not. Where did I say anything about circular?
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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.
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.
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