Cylindrical Definition and 821 Threads

A cylinder (from Greek κύλινδρος – kulindros, "roller", "tumbler") has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. It is the idealized version of a solid physical tin can having lids on top and bottom.
This traditional view is still used in elementary treatments of geometry, but the advanced mathematical viewpoint has shifted to the infinite curvilinear surface and this is how a cylinder is now defined in various modern branches of geometry and topology.
The shift in the basic meaning (solid versus surface) has created some ambiguity with terminology. It is generally hoped that context makes the meaning clear. Both points of view are typically presented and distinguished by referring to solid cylinders and cylindrical surfaces, but in the literature the unadorned term cylinder could refer to either of these or to an even more specialized object, the right circular cylinder.

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  1. P

    Calculating Volume of Solid Using Cylindrical Shell Method

    "simple" shell I know this is relatively simple, but I'm a little rusty. Could someone help me out? We want to find the volume of the solid obtained by rotating the region bounded by the curves y=x^4 and y=1 about the line y=7 using the cylindrical shell method. According to my book the...
  2. P

    Defining Vectors in Cylindrical Coordinates: Permissible Origin Point?

    is it leagal to define a vector with respect to the orgin in cylindrical coords? can a position vector to a point such as...(a, pi/4, pi/3) can u define a position vector <a, pi/4, pi/3>_o, o = (0,0,0)?
  3. P

    Fusion Experiment: Cylindrical Electrodes in Electrolyte Solution

    Anyone trying this experiment? Put a solid cylindrical electrode (anode/cathode) inside a hollow cylindrical or tightly coiled electrode (cathode/ anode) so that there is only a minimal ‘potential space’ between the two electrodes, and immerse them in a suitable electrolyte solution. The...
  4. P

    Music: conical vs cylindrical instruments

    a flute is cylindrical and when you hit the 2nd register (higher notes) the fingering is pretty much the same as on the base register. in other words, the jump is a regular octave. a clarinet is conical and the jump to the 2nd register is a 12 note jump from what i understand. can anyone...
  5. B

    How Is Volume Calculated Using Cylindrical Shells?

    Hi, I was hoping someone could check my work on a few problems and get me started on a few others. It involves definite integration, so I'm going to use (a,b)S as an integration symbol and P for pi. These are the ones I need checked: 1. Use cylindrical shells to find the volume of the...
  6. A

    How Do I Solve These Gauss' Law Problems for a Cylindrical Shell?

    I'm stuck on two problems. I hope someone can help me. Here they are... 1) For 1a I thought Q would be Q=\rho \pi L (b^2-a^2) but since \rho=\frac{k}{r} so Q=\frac {k \pi L (b^2-a^2)}{r}. After being stumped on 1a I'm not sure how to go about 1b. 2) I've derived about 4 equations for this...
  7. D

    Converting Spherical Equations to Cylindrical and Rectangular

    Question: (Note: p=rho and o=phi) Convert p(1-2cos^2(o))=-psin^2(o) into cylindrical and rectangular coordinates and describe or sketch the surface. The part that I don't know how to do is converting the spherical equation into cylindrical or rectangular coordinates. I know all the...
  8. D

    Converting Spherical Equations to Cylindrical and Rectangular

    Question: (Note: p=rho and o=phi) Convert p(1-2cos^2(o))=-psin^2(o) into cylindrical and rectangular coordinates and describe or sketch the surface. The part that I don't know how to do is converting the spherical equation into cylindrical or rectangular coordinates. I know all the...
  9. cepheid

    Gauss's Law: Cylindrical Symmetry

    Problem : A long coaxial cable carries a uniform volume charge density \rho on the inner cylinder (radius a ), and a uniform surface charge density on the outer cylindrical shell (radius b ). The surface charge is negative and of just the right magnitude so that the cable as a whole is...
  10. A

    Cylindrical shells trouble integrating

    i'm told to use the method of cylindrical shells to find the volume gnerated by rotating the region bounded these curves about the y axis: y=e^(-x^2) y=0 x=0 x=1 Couple questions. What does the graph of y=e^(-x^2) look like? Also, i know the integral is =integral(a,b) 2(pi)x*e^(-x^2) how...
  11. E

    Solving Torque and Tension for a Cylindrical Hoop with Mass and Radius R

    I have a cylindrical hoop of mass M and radius R with string (presumably thin and massless) wrapped around it. I take the end of the string from the hoop and let the hoop fall. (a) What is the torque about the CM of the hoop as a function of time? (b) What is the tension of the string as a...
  12. I

    Vector in cylindrical polar coordinates

    The problem is: Write the vector V=i+j+k=(1,1,1) at the point (x,y,z)=(1,1,1) in cylindrical polar coordinates. What is the gradient of the function phi=x(x^2+y^2)z at this point? Answer: I don't know how to write the vector in cylindrical polar coordinates. I know that the coordinates...
  13. X

    What is the equation of a cylinder with an angled axis and variable intercepts?

    What is the equation of a cylinder with its axis in the xy-plane and making an angle 'alpha' with the x-axis, the axis intersects the y-axis at a distance of 'k'? Initially i thought this problem to be very simple but haven't got any success with it in last few days thanks for your help! Xishan
  14. D

    Having some difficulty with a Trip. Integral in Cylindrical Coordinates

    Hi everybody The integral in question is the triple integral of x dV over the region E, where E is enclosed by the planes z=0, and z=x+y+3, and the cylinders x^2 + y^2 = 4 and x^2 + y^2 = 9. Well--- so far in cylindrical coordinates I know the r limits will be from 2 to 3 since the...
  15. F

    How Do You Convert Cylindrical Equations to Rectangular Form?

    I have the following cylindrical equation: z = r^2 cos(2theta) I am suppose to convert it into a rectangular equation. I'm stumped.
  16. S

    Cylindrical Tank Height Calculation (1587kg, 3.2m)

    I have been stumped on this question for two days~!~ I am not even sure this is where to post this, but any answers or ideas or anything are greatly appreciated! the question is 'CALCULATE THE HEIGHT OF A CYLINDRICAL TANK FILLED WITH WATER HAVING A MASS OF 1587.0 KG. THE DIAMETER OF THE...
  17. Y

    Type(s) of charge distribution for spherical and cylindrical gaussian surfaces

    I have a new question: "In applying Gauss's Law describe the types(s) of charge distribution for which (a) a spherical gaussian surface is useful and (b) a cylindrical gaussian surface is useful" please help!
  18. G

    Display a cylindrical surface in 3D using gnuplot

    I'm just beginning to learn to use gnuplot & can't figure out how to display a cylindrical surface in 3D. Even a simple one like x2 + y2 = 1 Oh, and how about a vertical plane? Anybody know how to do this?
  19. petmar

    Calculating Resonant Frequency of Water in a Cylindrical Pipe

    i have a cylindrical pipe with a fixed internal diameter and a variable length. how would i calculate the resonant frequency of water within it, given that the speed of sound in water is approx. 1398 m/sec?
  20. Jeebus

    How Do You Calculate the Volume of Liquid in a Horizontal Cylindrical Tank?

    I have to keep an inventory of how much is kept in a farm of tanks outside my school. The tanks are cylindrical, which would be no problem if they were standing on end, but they're not, they're lying on their sides. xx x x x----------x...
  21. denian

    Cylindrical Wavefronts: Linear Source Intensity at 60m

    for a linear source in three dimensions, the wavefront are cylindrical. and intensity, I is inversely proportional to r ( distance from the source ) is the fact given correct?? here's the question. cylindrical wavefronts are emitted by a linear source of length 4.0 m, at a rate of 50...
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