Cube Definition and 610 Threads

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.
The cube is also a square parallelepiped, an equilateral cuboid and a right rhombohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations.
The cube is dual to the octahedron. It has cubical or octahedral symmetry.
The cube is the only convex polyhedron whose faces are all squares.

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  1. Q

    Magnetic Field & Neodynium Cube: Strength Comparisons

    Does the magnetic field increase linearly with the number of magnets? For example, will 8 1/2 inch neodynium cubes have the same strength as a 1 inch cube? Thanks in advance
  2. K

    Discover the Intriguing World of 11-D Cube Images | Find Out More!

    Hello. Has anybody ever drawn an 11-dimensional cube (I mean, representation of 11-D cube in 2D)? Or does anybody have a picture of it? Thanks.
  3. 1

    Calculating Electric Flux through a Cube with a Moving Charge

    Homework Statement A surface in the shape of a cube with edge lengths a = 2.7 m is oriented in an x-y-z coordinate system so that the top and bottom faces are parallel to the x-y plane, the left and right faces are parallel to the x-z plane, and the front and back faces are parallel to the y-z...
  4. R

    Gauss's Law - Cube with point charge at centre

    Homework Statement a)A charge Q=10nC is placed at the origin, which is the centre of a cube with side lengths a=1cm whose faces are perpendicular to the x,y and z axis. What is the total flux through the box and what is the average of the perpendicular component of the electric field on the...
  5. P

    Cube root of 6 is irrational. (please check if my proof is correct)

    Prove that cube root of 6 irrational. Solution: I am trying to prove by contradiction. Assume cube root 6 is rational. Then let cube root 6 = a/b ( a & b are co-prime and b not = 0) Cubing both sides : 6=a^3/b^3 a^3 = 6b^3 a^3 =...
  6. C

    How Is Potential Calculated in a Non-Central Charge Within a Grounded Cube?

    Homework Statement There's a charge, not at the center of a grounded cube. Find the potential in the cube. Homework Equations The Attempt at a Solution I'm really just looking for a place to start. I should end up with some kind of series, but I don't know if I should be doing...
  7. M

    Electric flux through surface of a cube?

    Homework Statement A 10nC point charge is at the center of a 2mx2mx2m. What is the electric flux through the top surface of the cube? Homework Equations int(EA) = (Qin)/(ε0) The Attempt at a Solution int(EA) = EA + EA + EA + EA + EA + EA = 6EA A = 4m^2 Qin = 10nC ε0 =...
  8. B

    How Is Electric Flux Calculated Through a Non-Uniform Field in a Cube?

    Homework Statement A cube, placed in a region of electric field, is oriented such that one of its corners is at the origin and its edges are parallel to the x, y, and z axes as shown to the left. The length of each of its edges is 1.1 m. (a) What is the flux through the cube if the electric...
  9. E

    Nintendo game cube playing and whitch way works better upright or horazontal?

    I'm using my nintendo wii for my gamecube games and I just read in the maual that it's ok to remove the panels on the side to plug in the memory card and the controler if the system is horazontal whitch mine is I never done that before and I was woundering if it would hurt my system the maual...
  10. H

    How Do You Calculate the Net Gravitational Force on a Mass in a 3D Force System?

    Homework Statement A cube has an edge length of 2.0m. At each corner there is a different spherical mass. The masses are 1kg, 2kg, 3kg, 4kg, etc. u to 8kg. They Coordinate system: 1kg is at the origin and the 4kg, 2kg, and 8kg masses lie on the positive x, y, and z axis respectively. What...
  11. M

    Compressor with a displacement of 10 meter cube hour

    ]Hi Guys Can you help me with this : If a compressor with a displacement of 10 meter cube hour is displacing gas with a pressure of 10 bar, it is displacing 100 meter cube hour ?? (10 meter cube x 10 bar) rgds Marco
  12. C

    How Many Paths Can an Ant Take on a Cube with a Black Hole?

    Suppose an ant is on a vertex of a cube. On one of the three vertices neighboring the ant, there is a black hole. On each move, the ant travels to one of it's neighboring vertices, being careful not to pass through the black hole. The ant makes N moves in total. How many different paths lead the...
  13. R

    Electrostatics: cube with 3 charged walls

    Homework Statement There is a cube with a side length of 0,2m. Its three adjacent walls bear an area charge of -2nC/m2. Find the strength of the electric field at the center of the cube. Homework Equations E = \frac{\sigma}{2 \varepsilon _{0}} dE = \frac{\sigma dS}{4 \pi \varepsilon...
  14. K

    Distinct Colorings of a Cube: How Many Are There?

    Check it out: 'Each of the faces of the cube are colored by a diff erent of six fi xed colors. How many of the colorings are distinct?' I figured it would be 6!,very simple. But no,there's a trick, can u figure it out!
  15. F

    Thermal Expansion of Cube and Sphere

    Homework Statement A solid sphere and a solid cube are made from the same material. The sphere would just fit within the cube, if it could. Both begin at the same temperature, and both are heated to the same temperature. Which object, if either, has the greatest change in volume? The...
  16. E

    A question about standard metric cube

    Hi everybody, I'm having difficulties sizing a compressor for natural gas. First,my assumption is to take natural gas as mixture of ideal gases.The compression must be between 9 and 32 bar and it starts at 45 °C. I know that volumetric flow rate must be 85000 Sm3 per day ,where I assume 15°C and...
  17. M

    Magnetic Field Strength: Inverse Proportionality to Square or Cube?

    I have read a number of journal article that state that magnetic field strength diminishes inversely proportional to the square of the distance. BUT more than one has stated that the field strength is inversely proportional to the cube of the distance from the surface of the magnet. Which one...
  18. A

    Cool Coffee with Melting Ice Cube: Solve for T

    Homework Statement An insulated Thermos contains 190 cm3 of hot coffee at 83.0°C. You put in a 18.0 g ice cube at its melting point to cool the coffee. By how many degrees (in Celsius) has your coffee cooled once the ice has melted and equilibrium is reached? Treat the coffee as though it were...
  19. S

    Physical model for Completing the Cube?

    Completing the Square for finding the general solution for a quadratic equation by using a two dimensional drawing is easy. Since we can not so easily draw a three dimensional figure to help in finding a solution to a cubic equation, has any clever mathematician ever found a three dimensional...
  20. W

    Coulomb Force Point Charges on Cube

    Hello, I'm having a little trouble with this: Coulomb Force Point Charges on Cube Homework Statement Identical charges of Q (C) are located at the eight corners of a cube with side L (m). Show that the coulomb force on each charge has magnitude: 3.29Q^2/4\pi\epsilon_0l^2 Homework Equations...
  21. P

    Group of rigid rotations of cube

    I'm having trouble visualizing some of the rotations that compose this group. Clearly the group has 24 elements by argument any of 6 faces can be up, and then cube can assume 4 different positions for each upwards face. My book describes the rotations as follows: 3 subgroups of order 4...
  22. C

    A cube of some substance floats

    Homework Statement A cube of some unknown material floats in a pool of mercury. 43% of the cube is above the surface. Find the density of the cube.Homework Equations Fb=pVg d=m/VThe Attempt at a Solution So I Googled the density of mercury and found that it is 13,594 kg/m3. I also know that 57%...
  23. S

    Magnetic field at the center of a cube of wires

    Homework Statement Find the magnetic field at a point p in the center of the cube with side length 2b. Homework Equations Biot-Savart Law The Attempt at a Solution I attempted using the biot-savart law, but my answer contradicts what someone told us as a hint. Supposedly the...
  24. A

    26 is unique between a square (5^2) and a cube (3^3)

    i.e, a^{2} \pm 2 = b^{3} has (25,27) as the only solution. Now, can you prove it?
  25. M

    Algebraic Topology: Fundamental group of a cube

    How do you compute the Fundamental group of the 1-skeleton of the 3-cube I^{3} = [0,1]^{3} ? What about the Fundamental group of the 1- skeleton of the 4-cube I^{4} ? I know the Fundamental group of a space X at a point x_{0} is the set of homotopy classes of loops of X based at x_{0} . And...
  26. R

    Empty conducting cube with 4 sides at ground and 2 sides at V

    Homework Statement Empty cubic box of dimension "a" with conducting walls. Two opposite walls are held at a constant potential V, while the other walls are grounded. Find an expression for the electric potential inside the box. (Assume box centered on the origin, walls are all normal to one...
  27. S

    Chain rule derivative applied to an ice cube

    Homework Statement A cubical block of ice is melting in such a way that each edge decreases steadily by 9.8 cm every hour. At what rate is its volume decreasing when each edge is 10 meters long? Homework Equations V(t) = (l(t))^3 m^3 l'(t) = 0.098 m/h The Attempt at a Solution...
  28. X

    Electron in dielectric cube (Quantum Mechanics)

    Homework Statement [PLAIN]http://img408.imageshack.us/img408/1685/wergp.png Homework Equations H\psi = E\psi The Attempt at a Solution For part a) I used H\psi = E\psi to get: E = \frac{\widehat{p}}{2m} + \frac{Kx^2}{2} + \frac{e\Phi_o}{a}x and assuming E = Q? and rearranging for K...
  29. A

    Volume of Cube changing with respect to time.

    Homework Statement The volume V of a cube with sides of length x in. is changing with respect to time. At a certain instant of time, the sides of the cube are 5 in. long and increasing at the rate of 0.1 in./sec. How fast is the volume of the cube changing at that instant of time? The...
  30. L

    Volume of a cube as a function of surface area

    Homework Statement Express the volume of a cube as a fuction of the total surface area Homework Equations Surface area = 6x^2 Volume = x^3 The Attempt at a Solution So, we need to manipulate the surface area equation so we can use it to find volume right? SA = 6x^2...
  31. C

    Resistance calculation in a cube

    Homework Statement each edge of a cube is built with a one ohm resistor, body diagonals are also built with one ohm resistors each. find out equivalent resistance across any two adjacent vertices. Homework Equations i guess it deals with star and delta transformations The Attempt at...
  32. J

    Thermodynamics ice cube problem

    First of all, hi, and thanks ahead of time... I've been working on this homework for almost a week, even asked the teacher for help but still haven't been able to figure out what I've been doing wrong/missing. its online work so ill copy paste it Homework Statement (a) Two 32 g ice cubes...
  33. T

    Calculating flux when charge on vertex of cube

    Homework Statement A point charge q = 112 x 10^-9 C is placed at the centre of a cube of side l = 0.2 m. If the charge is moved all the way to one vertex of the cube, determine the flux through each of the faces. Homework Equations None. The Attempt at a Solution I looked at...
  34. D

    Pythagoras and Vector coordinates of a cube.

    Homework Statement Basically we are given the coordinates for A=(13.0492, 30.9498, 9.01115) and C=(1.97687, 4.68868, 17.3632) which are two top corners of a cube that is sunk in the ground partway (specifically it's based on the cube near the Melbourne museum). But we don't know where the...
  35. Spinnor

    Square with edges, cube with faces identified.

    Say I randomly give each edge of a square a direction and then I identify opposite edges, do I always come up with a two-dimensional compact manifold without boundary? Seems there are eight different edge orientation assignments, many being equivalent? How many different spaces? Can I do the...
  36. N

    Moment of inertia for a hollow cube. Rotating about diagonal opp corners

    Hi Folks, I am designing a piece of kinetic scultpure that will involve cubes made from aluminium square tubing rotating around an axis that passes through two diagonal corners. I am trying to determine motor size to drive this thing, and to do that I need to know its moment of inertia. Math...
  37. A

    Need to find the volume of a rounded cube.

    Hello everyone. I'm currently working on a project (independent study and not homework) and I find myself having to calculate the volume of a cube with rounded corners and I'm stumped. Any help would be really appreciated. The cube itself is 8 cubic meters (2m on each side) and the rounded...
  38. H

    Fluid Mechanics : Ice cube melting and Surface Energy Que.

    Q. 1. if a ice cube is placed in a container containing liq on which it is floating. then is it possible that after ice melts, water level rises in vessel in any particular case. 2.Does heat evolves when water rises in a capillary. and how much heat is evolved in height of liq in capillary...
  39. Loren Booda

    How can you fill the cube to one-sixth its volume?

    Given only water and a cubic container with one open face, how can you fill the cube to one-sixth its volume?
  40. T

    Angular momemtum with a puck and ice cube

    Homework Statement A 100 g puck is attached by a length of string to a 500 g block of ice. The string passes through a hole in the centre of a horizontal, frictionless table, and, because it is revolving in a circle of radius 20 cm, the puck is able to support the ice. (Refer to attachment...
  41. H

    Fluid Mechanics : Ice cube melting and Surface Energy Que.

    I have a que. if a ice cube is placed in a container containing liq on which it is floating. then is it possible that after ice melts, water level rises in vessel in any particular case. Does heat evolves when water rises in a capillary. and how much heat is evolved in height of liq in...
  42. J

    How Do You Calculate Total Flux Through a Cube with Non-Uniform Electric Field?

    Homework Statement A cube has lengths L. E(x) = {a(x+L)2i - (ayL)j where a is constant Find the total Flux through the cube. Homework Equations The Attempt at a Solution i know the flux is 0 through the z = 0 and z = L planes but the other sides and the top & bottom i am...
  43. C

    Finding the Coefficient of Static Friction for a Cube

    Homework Statement A cube of side l rests on a rough floor. It is subjected to a steady horizontal pull F, exerted a distance h above the floor as shown below. As F increases, the block will either begin to slide, or begin to tip over and thus rotate. Determine the coefficient of static...
  44. J

    How Is Electric Flux Calculated for a Non-Uniform Field in a Cube?

    Homework Statement Consider a cube of sides L. Suppose that a non-uniform electric field is present and is given by E(x) = {a(x+L)^2}x - (ayL)y where a is a constant. a) determine the elctric flux through the face of the cube that lies in the xy plane at z = 0 (express answer in a & L...
  45. H

    Proving the Three Cube Roots of 1 with w

    Homework Statement Let w be a primitive cube root of 1. show that 1, w,w^2 are the three cube roots of 1. Homework Equations The Attempt at a Solution I'm not quite sure how to even start this. any help will be greatly appreciated.
  46. D

    Angle between two diagonals of a cube.

    Find the angle between the diagonal of the back and left faces of a cube with one vertex on the origin A) 60 degrees B) cos^-1(1/sqrt(6)) C) cos^-1(1/3*sqrt(2)) D) 90 degrees E) 120 degrees The two diagonals eminate from the vertex at the origin. I will write [u] to mean the "norm"...
  47. M

    Angle between two diagonals of a cube.

    Find the angle between the diagonals of the back and left faces of a cube with one vertex on the origin. A) 60 degrees B) arcos(1/sqrt(6)) C) arcos(1/(3sqrt(2)) D) 90 degrees E) 120 degrees. I think the answer should be D) 90 degrees. Since these vectors are diagonals on the face of the cube...
  48. I

    N-dimensional cube problem with clever solution?

    Homework Statement http://img202.imageshack.us/img202/4535/asdty.jpg Homework Equations I think the relevant equations are the divergence theorem [PLAIN]http://upload.wikimedia.org/math/0/9/b/09b08625d572f4d7c9ceb7585241dc36.png The Attempt at a Solution Since it hints at a...
  49. B

    Electric flux through cube with nonuniform electric field

    Homework Statement A closed surface with dimensions a=b=0.400m and c=0.600m is located as shown in the figure (be aware that the distance 'a' in the figure indicates that the rectangular box sits distance "a" from the y-z plane). The electric field throughout the region is nonuniform and...
  50. T

    Thermodynamics, heat in a copper cube transfer to water

    Homework Statement When a copper cube of side of 2.0 cm is immersed into a perfectly insulated container filled with 1.0 kg of water at 5 degree celcius , the temperature of water rises to 7 degree celcius . Assuming that no heat is lost to the surrounding , calculate the original...
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