What is Cube: Definition and 609 Discussions

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. L

    Is cast iron a Body and Face Centered Cube structure?

    Homework Statement is cast irion body and face centenerd cube structure? wasnt quiet sure, i thought it was both because it can solidify different temperatures one of them Homework Equations mululpe different cast irons The Attempt at a Solution
  2. CptXray

    How can I solve a Laplace equation in a cube with mixed boundary conditions?

    Homework Statement There's a metal cunducting cube with edge length ##a##. Three of its walls: ##x=y=z=0## are grounded and the other three walls: ##x=y=z=a## are held at a constant potential ##\phi_{0}## . Find potential inside the cube. Homework Equations The potential must satisfy Laplace...
  3. J

    Maximum and minimum speeds in a moving cube

    Homework Statement A rigid cube in the figure moves in space. At a certain time ##t## its front face ##ABCD## is vertical and the velocity of vertex ##A## is vertical down ##v## while the velocity of its vertex ##D## makes an angle with the vertical and has magnitude ##v_{2}## while lying on...
  4. jim mcnamara

    Why do wombats have cube-shaped poop?

    http://meetings.aps.org/Meeting/DFD18/Session/E19.1 link to presentation https://gizmodo.com/we-finally-know-how-wombats-produce-their-distinctly-cu-1830414749 This may belong in Fluid dynamics. It is begin presented at an APS Fluid Dynamics seminar. @boneh3ad might know more. Wombats...
  5. C

    A cube tipping over on an inclined plane

    What's the minimal angle of a ramp such that a cube with side 10 cm placed on it will tip over? The coefficient of friction between the cube and the ramp is 0.6. I have given it some thought and I have come to certain conclusions: I think that the cube will tip over once the force of gravity...
  6. C

    Answer: Terminal Temperature of Water with Ice Cube

    We have a glass containing 0.5 liter (0.5 kg) of water whose temperature 100 degrees Celsius. We also have an ice cube with mass 0.01 kg and temperature -10 degrees Celsius. The cube is put into the glass. The glass is then insulated from the outside world, until the cube has melted. What will...
  7. Krushnaraj Pandya

    Electric field and potential at vertex of cube

    Homework Statement A solid non-conducting cube of side l and uniformly distributed charge q, has electric field E and potential V at one of its vertex, imagine this cube to be made of 8 smaller cubes of side l/2. if one such cube is removed, find the new field and potential at the point where...
  8. T

    I Proof that cube roots of 2 and 3 are irrational

    Proof by contradiction that cube root of 2 is irrational: Assume cube root of 2 is equal to a/b where a, b are integers of an improper fraction in its lowest terns. So the can be even/odd, odd/even or odd/odd. The only one that can make mathematical sense is even/odd. That is...
  9. CDL

    Electric Flux through the Face of a Cube

    Homework Statement Griffiths' Introduction to Electrodynamics problem 2.10, Homework Equations Gauss' Law, ##\int_{S} \textbf{E}\cdot \textbf{dS} = \frac{Q_{\text{enc}}}{\epsilon_0}##[/B]The Attempt at a Solution It seems reasonable that the flux through the shaded surface and the front...
  10. S

    Hydrostatics: Immersing a metal cube in water......

    Homework Statement A metal cube is placed in an empty vessel. When water is filled in the vessel so that the cube is completely immersed in the water,the force on the bottom of the vessel in contact with the cube (A) will increase (B)will decrease (C)will remain same (D) will become zero...
  11. M

    Will a Sealed Steel Container Float in the Ocean?

    Homework Statement A large sealed container full of air falls into the ocean. It has internal dimensions of 6.06 2.59 2.43 m, with walls made of steel (8050 kg m3 ) which is 2.00 cm thick. Does it float? Homework Equations FBuoyancy = density*volume*g weight = mg m = density*volume density of...
  12. J

    Reference to this formula X = cube root of R

    Hi, Sorry for this weird question. My computer crashed and also the notes in it. I had a book wherein I'd written all the formulae. There is one formula in notes of Power System. X = cube root of R. I remember there was a website that even had its derivation, but I don't have the bookmarks...
  13. Ari

    How to find period of a SHM concerning a cube and spring?

    1. Homework Statement The 4.00 kg cube in the figure has edge lengths d = 8.00 cm and is mounted on an axle through its center. A spring ( k = 1400 N/m ) connects the cube's upper corner to a rigid wall. Initially the spring is at its rest length. If the cube is rotated 4.00° and released, what...
  14. Monoxdifly

    MHB Calculating G's Distance from BH on an ABCD.EFGH Cube

    In an ABCD.EFGH cube whose side length is 8, the distance between the point G and the line BH is ... A. 4 cm B. 4\sqrt2 cm C. 4\sqrt3 cm D. 8\sqrt2 cm E. 8\sqrt3 cm I got \frac{8}{3}\sqrt6 cm. Do you guys get the same answer?
  15. Monoxdifly

    MHB Finding the Distance from Point P to AC on an ABCD.EFGH Cube

    Given an ABCD.EFGH cube whose its side length is 8 cm. The point P is within AB so that AP = 3PH. The distance between P to AC is ... A. 2\sqrt3 cm B. 3\sqrt3 cm C. 2\sqrt6 cm D. 3\sqrt6 cm E. 4\sqrt6 cm So AH is 8\sqrt2 cm and PH = 6\sqrt2. What do I do now? Is the triangle HPC a right triangle?
  16. K

    Finding the ratio of the volumes of a cube and a sphere

    Homework Statement Homework Equations Volue of a sphere: ##~\displaystyle V=\frac{4}{3}\pi r^3## Area of a sphere: ##~\displaystyle A=4\pi r^2## Minimum/Maximum occurs when the first derivative=0 The Attempt at a Solution The fixed area is k, the edge is a: $$6a+4\pi...
  17. T

    I Doubling a Cube: Can 3D Geometry Help?

    In plane geometry it is impossible to construct a line equal to the (cube root of 2) times the length of a side of a cube, making it impossible to double a cube with a compass and straight edge. Maybe plane geometry needs one more dimension. What happens if we extend the geometry to 3D(solid...
  18. E

    Cube balanced at equilibrium about two different axes

    Homework Statement A cube balanced with one edge in contact with a table top and with its center of gravity directly above the edge is in _______ equilibrium with respect to rotation about the edge and in _________ equilibrium with respect to rotation about a horizontal axis that is...
  19. T

    Electric flux of a cube due to a point charge

    Homework Statement Homework Equations Gauss's Law The Attempt at a Solution I simply used logic and observed the symmetry of the cube. If the charge is placed on the middle of the cube, the flux would simply be Q/∈0. The face of the cube itself can be split into 4 squares, with the charge at...
  20. Jay Macarus

    I Calculate the distance between two cleaved crystals

    Hey guys, can't seem to make sense of this question from phys. It goes.. "A crystalline solid consists of atoms stacked up in a repeating lattice structure. Consider a crystal as shown in Figure a. The atoms reside at the corners of cubes of side L = 0.200 nm. One piece of evidence for the...
  21. Pushoam

    Elec. flux through the top side of a cube with q at a corner

    Homework Statement Find the electrix flux through the top side of a cube. The cube's corner is on the origin, and is 'a' units on length. The charge 'q' is located at the origin, with the corner of the cube. Homework Equations Gauss's law and symmetry The Attempt at a Solution I take 8 cubes...
  22. M

    Force on the bottom of the vessel containing a submerged cube

    Homework Statement Conside the fig below. A tank of water (height of water column b) is kept on a electronic weighing scale . a metal cube (side a and density D) is hung from a spring balance and the spring balance is slowly lowered into the tank till the cube reaches the bottom of tank. The...
  23. B

    B "Mysterious" beamsplitter cube

    I'm using a non-polarizing beamsplitter cube in an experiment, but it's behaving in an unexpected way. I expected that, if a laser beam enters the cube from one side, ~50% of the beam passes through the cube in the same direction, while ~50% of the beam is reflected and exits the cube at a...
  24. O

    B Calculate length of side of cube

    How can I calculate the length L of each side of a cubic simulation box with 500 molecules (in Ångstrøm) when I want molar volumes of V1 = 0.6 l/mol?
  25. berkeman

    Are there standard axes/orientations for Rubik's Cube game programs?

    I did a PF search to try to see if this was discussed before, and didn't find what I was wanting to ask about (I could have missed it). :smile: I'm writing a Rubik's Cube game C/C# program for fun (starting with a console app and working up through various GUI options). I'd like to use a...
  26. S

    Buoyancy: Cube of Iron - solved this correctly?

    Hi, Just wondering if I'm going about solving this problem correctly: "A block of iron quickly sinks in water, but ships constructed of iron float. A solid cube of iron 1.6 m on each side is made into sheets. From these sheets, to make a hollow cube that will not sink, what should the minimum...
  27. S

    Conservation of Energy and Angular Momentum in Inverse Cube Force Problems

    Homework Statement I'm given a force law is F = \frac{-k}{r^3} and that initially, the particle is in a circular orbit the particle is given an impulse parallel and in the opposite direction to its velocity find the distance from the center for the particle as a function of time. Homework...
  28. O

    Lagrangian of system with circle and cube

    Hello. I have some problems with making Lagrangian. I need your advice. 1. Homework Statement I have this situation: Consider the circular path is intangible and without friction. I have to find Lagrangian for coordinates x and θ. Homework Equations [/B] L = U - V The Attempt at a...
  29. lfdahl

    MHB A cube with 9 interior points: Show that at least two of them are less than √(3)/2 apart.

    There are $9$ points in the interior of a cube of side $1$. a) Show that at least two of them are less than $\frac{1}{2}\sqrt{3}$ apart. b) Can $\frac{1}{2}\sqrt{3}$ be replaced by a smaller number?
  30. D

    Electric Flux through Cubical Surface Enclosing Sphere

    Homework Statement A uniform charge density of 700 nC/m3 is distributed throughout a spherical volume of radius 6.00 cm. Consider a cubical Gaussian surface with its center at the center of the sphere. [reference picture] What is the electric flux through this cubical surface if its edge...
  31. A

    How Are Friction and Angular Velocity Related in the Cube on Funnel Problem?

    I've uploaded a picture instead of writing the whole problem. So the forces to consider here are - the weight of the cube, the normal force exerted on it by the funnel surface in contact, the centripetal force, and the frictional force. If there is no relative motion between the cube and the...
  32. D

    Electric Field of a cube with a rod

    Homework Statement The electric field at 2 cm from the center of long copper rod of radius 1 cm has a magnitude ##3 \frac{N}{C}## and directed outward from the axis of the rod. (a) How much charge per unit length exists on the copper rod? (b) What would be the electric flux through a cube of...
  33. L

    B Generalized Linear equation of a cube

    As per my understanding, a linear equation with two variables form a line segment (ax=by+c or ax+by=c) and linear equation with three variables form a plane (ax=by+cz+d or ax+by+cz=d). Am I right? And if I am right, does an equation with four variables form a cube?
  34. Kaneki123

    A Question about Sound Waves Propagating Through a Large Metal Cube

    Okay, I have a very simple question that...Suppose we have a very wide cube(dense and hard)...We place two persons at each of its ends...One the persons strikes its surface at one end. Now this person A will hear the sound due to vibrations of that end's surface (which further vibrate the air...
  35. Z

    Length of an Edge of a Cube

    Homework Statement The volume of a cube is 'v' cubic yards, and its surface area is 'a' square feet. If 'v' = 'a' what is the length in inches of each edge?Homework Equations volume of a cube = e^3 surface area of cube = 6e^2The Attempt at a Solution volume of a cube = 'v' cubic yards...
  36. G

    A cube of side L=2 m is made of a cooper cable with 2mm^2

    Homework Statement A cube of side L=2m is made of a cooper cable with 2mm^2 of cross section area. 1) Find the electric resistance of one side of the cube. 2) Find the equivalent resistance in between the points A and B.
  37. D

    Solving Heat Transfer Problem with Melting Ice Cube

    Good day members of physics forums . I am a university student currently studying thermodynamics and I just am a bit confused about a heat transfer problem. If you have the following items: 1 metal container which is well insulated from the outside ; ; 1 quantity of water and an icecube ...
  38. D

    B (Hypothetical) 6ft hardened-steel cube dropped at 100 meters

    During a random conversation with a friend, we got onto the subject of dropping a 6ft cubed cube of Hardened-Steel from the height of 100 meters. I ended up getting really curious about the energy it would cause, as well as the potential impact/destruction it would cause on the area...
  39. D

    Multiple reflections and transmissions of light inside a cube

    Imagine I have a 10x10x10cm cube filled with a scintillating material (material capable of generating light when energized). Three cameras are looking at this cube from three orthogonal directions (x, y, and z). Light is generated inside the cube and is refracted as it leaves the cube and...
  40. J

    Force required to immerse a wooden cube

    Homework Statement The force required to immerse a wooden cube of side 4 cm and relative density RD 0.5 completely in water is 1) 16x10-3 kgwt 2) 32x10-3 kgwt 3) 64x10-3 kgwt 4) 128x10-3 kgwt Homework EquationsThe Attempt at a Solution Density of the cube = 0.5 gcm-3 Volume of cube = 64 cm3...
  41. C

    I Stress exerted on a wooden cube dropped on concrete floor

    I wonder if it is possible to at least estimate the stress (or the impact force) that the cube in question will experience due to the collision with the concrete floor. Assumptions: 1. The cube is dropped from height h 2. The cube is relatively small, thus we can neglect air resistance...
  42. Const@ntine

    Thermodynamics: Steam is added to an ice cube

    Homework Statement Vapors of 100 C is added to an ice cube of 0 C. How much of the ice cube has melted and what's the final temperature if the masses of the steam and the ice cube are 10.0 g & 50.0 g respectively? Homework Equations Lw = 3.33 x 105 J/kg cw = 4186 J/kg*C Q = m*c*ΔΤ Q =...
  43. Y

    Electrostatic potential of a cube with charge density

    Homework Statement Consider a uniformly charged cube with uniform charge density ρ.The ratio of electrostatic potential at the centre of the cube to that of one of the corners of the cube is? A hint on how to approach the problem's solution would be appreciated.(whether to use gauss law or not...
  44. Daniel McKinley

    How to simplify cube root expression

    ]Homework Statement Solving the cubic equation x^3 + 6x = 20 by using formula gives (10+ sqrt(108))^1/3 - (-10 + sqrt(108))^1/3 How do you show that this comes out exactly 2? No calculators allowed.Homework EquationsThe Attempt at a Solution Tried cubing the expression and tried using the...
  45. Z

    Heat question -- Ice cube in a cup of water....

    Homework Statement An ice cube of mass 0.01.kg at a temperature of 0 degrees Celsius is dropped into a cup containing 0.10kg of water at a temperature of 15 degrees Celsius. What is the max estimated change in temperature of the contents of the cup? SHC of water = 4200J per kg per kelvin...
  46. Math Amateur

    MHB Finding the Cube Root of 2: Can You Solve It?

    EDIT ... ... SOLVED ...Can anyone help me with displaying the cube root of 2 as shown in the example below taken from Dummit and Foote, Section 13.4 ...https://www.physicsforums.com/attachments/6605Help will be appreciated, Peter*** EDIT *** Just found what I think is the solution ... it's...
  47. M

    MHB Square Root vs Cube Root

    I know that x^2 = 4 yields two answers: x = -2 or x = 2. I also know that x^3 = 8 yields x = 2. Question: Why does the square root yield both a positive and negative answer whereas the cube root yields a positive answer?
  48. M

    MHB Calculating the Sixth Root of 3

    Let cbrt = cube rootcbrt{3} x cbrt{3} = (3)^(1/3) * (3)^(1/3) 3^(1/6) ir sixth root {3} Correct?
  49. BillTre

    Where Can I Find a 1 mm Cube for Visual Demonstrations?

    I am looking for a nice looking 1 mm cube to use in a video I want to make. I am looking for suggestions about possible sources. I don't really want to mess around with making one right now and I would prefer (at least now) practical effects to using a 3D animation program. So far I have only...
  50. B

    I Ave length of intersection of all lines through a unit cube

    I'm having trouble even beginning to figure out how to approach solutions for this. I begin with a unit cube, and imagine all the possible lines that intersect the cube. I am assuming there must be an average length of these intersections; I want to find that average length. Another way to...
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