Which dimension of the cylinder is more important when figuring the volume, the diameter or the length? Why?
I had a feeling it would be the diameter but I don't really know why...
(The volume of a cylinder is 3.14(r)^2 (length)
2007-01-28 04:49:07 · 9 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Both dimensions are equally important components of the formula, neither has a greater priority.
2007-01-28 04:59:52 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Not sure what you really mean, since both dimensions are necessary to know the volume. However, since the volume is proportional the square of the diameter while only linearly proportional to the length, it is more senstive to the diameter measurement.
2007-01-28 12:54:03 · answer #2 · answered by . 4 · 0⤊ 0⤋
When you double the diameter, the volume increases by a factor of 4. When you double the lenght, the volume increases by a factor of two. Does it mean the diameter is more important?
2007-01-28 12:56:04 · answer #3 · answered by sahsjing 7 · 0⤊ 0⤋
The diameter because the area of the base is given by pi x r^2.
If there is an error in the diameter, there is an error in the radius measurement, and that error is squared in the final result.
2007-01-28 13:03:15 · answer #4 · answered by davidosterberg1 6 · 0⤊ 0⤋
both the length and diameter are equally important......without one, the volume would remain as a variable.
2007-01-28 12:56:52 · answer #5 · answered by iron muncher 3 · 0⤊ 0⤋
I would say "The diameter, because an error δd of its value would influence the final result more than an error δl in length - an error in diameter would mean a "squared error" of (d^2), let alone radius",
but I do believe it depends on the error each one brings.
I mean, if you use
total error = sqrt [((θv/θl)δl)^2+(θv/θd)δd)^2] where
θv/θl=pi (d/2)^2, while θv/θd=pi l d/2, then
If you use the same instrument to measure d, l, then δd=δl and
total error = sqrt [((θv/θl)δl)^2+(θv/θd)δd)^2]
= sqrt [((Ï d^2/4)δl)^2+(Ï l d/2 δl)^2]
= sqrt [(Ï d/2 δl)^2 (l^2+ (d/2)^2)], so you have to compare l and d
2007-01-28 13:27:07 · answer #6 · answered by supersonic332003 7 · 0⤊ 0⤋
neither of them are important. to find the volume of a cylinder, you need to be the cylinder. That's the most important dimension of all.
2007-01-28 12:54:55 · answer #7 · answered by David 3 · 0⤊ 1⤋
both are equally important. without them, it would be impossible to find the volume
2007-01-28 12:52:52 · answer #8 · answered by Anonymous · 0⤊ 0⤋
you need both
2007-01-28 12:52:50 · answer #9 · answered by gggjoob 5 · 0⤊ 0⤋