For x ≥ 1, the surface area of revolution of y = 1/x is infinite, yet the volume is finite. How is it possible that it cannot even contain the paint required to paint it?
2007-07-20 11:20:38 · 5 answers · asked by Scythian1950 7 in Science & Mathematics ➔ Mathematics
Alexander, thanks for having pointed that out.
2007-07-20 11:21:31 · update #1
Well, since surface area is two-dimensional, the assumption would have to be that the coat of paint is infinitely thin. So, you have a coat of infinite area, but the thickness of the coat is zero. And, of course, infinity times zero can be anything.
2007-07-20 12:14:09 · answer #1 · answered by Anonymous · 1⤊ 0⤋
The thing after it is revolved looks like a weird spike. At a large distance from the center, the spike kind of flattens all the way to the ground, and therefore is containing practically no volume, but still holds surface area. The volume can be found using hard math (don't ask me how), but the surface area is infinite
2007-07-20 18:35:01 · answer #2 · answered by Felix S 2 · 0⤊ 0⤋
It cannot contain the paint becuase of the infinitesimal
orifice at the end of the horn at infinity, through which
the paint leaks.
2007-07-20 18:50:01 · answer #3 · answered by Alexander 6 · 0⤊ 0⤋
The volume is NOT really finite. It only approaches a finite number - pi.
Keep in mind that to find the volume, one must use integration. Improper integrals are defined using limits, and this is an improper integral so it is no exception. It is not a finite volume.
2007-07-20 18:38:44 · answer #4 · answered by whitesox09 7 · 0⤊ 1⤋
It just is. A classic example of how math is so cool.
2007-07-20 18:35:40 · answer #5 · answered by The Prince 6 · 4⤊ 0⤋