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. 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...
  2. DaMeekie

    B What are the properties and equations of a 4-dimensional cube?

    We all have a pretty good understanding about our three dimensions. First starting off with 0D or a point in space = 360º. Then 1D being a line = 180º. Moving to 2D such as a square = 90º. Finally ending with 3D = 45º. It is important to state that finding these angles requires the viewer to...
  3. J

    Net electric flux through a Gaussian cube

    Homework Statement An electric field given by https://edugen.wileyplus.com/edugen/shared/assignment/test/session.quest2560893entrance1_N10030.mml?size=14&ver=1486488694211 =...
  4. V

    I Infinitesimal cube and the stress tensor

    The Cauchy stress tensor at a material point is usually visualized using an infinitesimal cube. The stress vectors (traction vectors) on opposite sides of the cube are equal in magnitude and opposite in direction. As a result, the infinitesimal cube is in equilibrium. However, when we derive...
  5. W

    Water level before and after metling of ice cube

    Homework Statement A big ice cube is placed in a small glass of water. The level of water in the glass is marked. When the ice cube melts completely,the overall water level will remain the same. Explain. Homework Equations Upthrust= weight of fluid displaced The Attempt at a Solution Since...
  6. C

    Ice cube sliding off metal roof

    Homework Statement Homework Equations $$mgh = \frac{1}{2}v^2$$ The Attempt at a Solution [/B] I'm working on a). I tried using conservation of energy to get v. $$mg(c+b) = \frac{1}{2}v^2$$ $$v = \sqrt{2g(c+b)}$$ After this I'm stuck. In order to get distance from knowing the velocity...
  7. MarkFL

    MHB Symmetry Groups of Cube & Tetrahedron: Orthogonal Matrices & Permutations

    This question was originally posted by ElConquistador, but in my haste I mistakenly deleted it as a duplicate. My apologies... For part (a) we can define two cyclic subgroups of order $2$, both normal, $\langle J\rangle$ and $\langle K\rangle$ such that $V=\langle J\rangle \langle K\rangle$...
  8. Thiru07

    How do I approach this problem? (Cubes within a larger cube....)

    Homework Statement A cube of 8cm x 8cm x 8cm is divided into smaller cubes of 1cm x 1cm x 1cm and all the smaller cubes are numbered and arranged to form the larger cube. The smaller cubes are numbered such that the number on the cube represents the smallest volume enclosed by extending the...
  9. BiGyElLoWhAt

    Current flow direction in "infinite" cube of 1ohm resistors

    Homework Statement Write a program to find the equivalent resistance between two opposite corners within a grid of "infinite size" with resistors between each point. So basically we have an infinite cube made up of cubes with 1 ohm resistors between each node. Homework Equations Kirkoff's laws...
  10. H

    Quanser cube servo, any expereince with it?

    does not come cheap. looks like a great educational device to teach control. anyone use it? http://sine.ni.com/nips/cds/view/p/lang/en/nid/212417
  11. caffeinemachine

    MHB Composition by the Cube Root is Smooth

    Let $f:\mathbf R\to \mathbf R$ be a smooth map and $g:\mathbf R\to \mathbf R$ be defined as $g(x)=f(x^{1/3})$ for all $x\in \mathbf R$. Problem. Then $g$ is smooth if and only if $f^{(n)}(0)$ is $0$ whenever $n$ is not an integral multiple of $3$. One direction is easy. Assume $g$ is smooth...
  12. alexmahone

    MHB In how many ways can a cube with 8 different vertices be oriented?

    My solution: Imagine that we have 8 points in space which must be occupied by the vertices of the cube. Let A be one of the points. Fix anyone of the vertices at A. This can be done in 8 ways. We have 3 different choices for an adjacent point (say B) because each vertex of a cube is connected...
  13. Blockade

    Need help in Electric Flux within a cube with Gauss' Law

    Homework Statement I need help in figuring out if I have done this problem correctly. From what I understand ∫E * dA = E*A, where E is the electric field and A is the area of a side. My biggest concern is if I can plug in the length "L" for the "x" and "z" variables within "E = -5x * E0/L i +...
  14. U

    I What do you call a parallelepiped that isn't a cube?

    I was curious what you would call a parallelepiped that isn't a cube and isn't a rectangle and isn't just a rhombohedron? Here is my problem...I need to describe an oblique/tilted parallelepiped but if I just say 'parallelepiped' that would include a cube or rectangle (which I am not referring...
  15. J

    How Much Flux Passes Through a Square in a Non-Uniform Electric Field?

    Homework Statement Consider an electric field E = 2x i - 3y j. The coordinate x and y are measured in meters and the electric field is in N/C. What is the magnitude of the flux of this field through a square whose corners are located at (x,y,z) = (0,2,0), (2,2,0), (2,2,2), (0,2,2)? Homework...
  16. K

    Water level change for melting ice cube

    Homework Statement http://imgur.com/Sk6YkIf . You can take Va to be volume of cavity and Di to be density and Vo to be volume of cube and A to be surface area of container and h to be height of liquid column and Vi to be volume of immerser part of cube. Prove if water level will rise or will...
  17. W

    Non-uniform electric field flux through a cube

    Homework Statement A cube side length a=2 has one vertice at the origin of the referencial. an electric field is present described as follows: E(x,y,z)= (2xz) i + (x+2) j + (y(z^2-3) k Find the flux through the cube My cube's front face is at (0 to 2, 0, 0 to 2) Homework Equations flux=∫E.dA...
  18. Ravi Singh choudhary

    Hydrostatic stress on cube placed in deep sea

    Ques: If one metal cube placed in deep sea where will be maximum shear stress in cube? What I know: In hydrostatic condition there would be no shear stress, that means on any face of cube there would be not shear stress at all. In case of two dimensional stress; if we have same...
  19. N

    MHB How to Find the Cube Root of a Number?

    Hello! My book explained how to take cube root of a number withou using calculator. I managed to extract the cube root of number less than a million. But when its higher like this one 12812904. I cannot extract it. Can you suggest an algorithm on how to go about this one? Thanks!
  20. T

    Does this cube slide or topple?

    I have attached a copy of the full question and my diagram which I thought was correct but it does not give me the correct answer. The answer for (i) is that it stays put and for (ii) that it topples. I do not get = 0 for any of them. I get some values... (i) -0.15 for slide, 0.346 for topple...
  21. F

    [Rotational dynamics] cube sliding on a dish

    1. Homework Statement A small cube is sliding on a round dish (see attached figure) . The cube is always in contact with the (vertical) edge of the dish (which prevents the cube from falling outside the dish itself). There is friction between the cube and the dish. The dish can rotate around...
  22. I

    MHB Angle between two line segments of a cube.

    Given a cube, choose a vertice and draw 2 of the three possible diagonals. What is the measure of the angel between those two diagonals? Proposed answer: We can say that both diagonals touch vertice A, to give it a name. We can also call the endpoints of both diagonals B and C. If we imagine...
  23. kaliprasad

    MHB Perfect Cube & Square: 5-Digit Number

    Find 5-digit number whose half is a perfect cube and one-third is a perfect square
  24. vinamas

    Calculating Buoyancy Force & Length of Submerged Cube

    Homework Statement A layer of oil that has a density of 930kg/m^3 is floating on the surface of water in a container if a wooden cube with a length of 4 cm becomes submerged where it's lower half is in water and it's upper half is in oil the cube's density is 960kg/m^3 find A) the buoyancy...
  25. J

    Does the Inverse cube law apply for magnetic repulsion?

    Was just wondering is it only possible for magnetic attraction? because the force increases exponentially with decreased distance, or can it be used for repulsion. It's blatantly obvious that magnetic repulsion is a lot weaker than attraction, by a 10% margin. hence why repulsion is weaker, but...
  26. vinamas

    Wooden Cube submerged length and the carry limit

    Homework Statement A wooden cube with the length of 10 cm is and a density of 700 kg/m^3 is floating on water A)Find the submerged parts length of the cube B) find the maximum added mass to the block before it becomes totally submerged Homework Equations FB=density*volume*gravity FB=Fg...
  27. M

    B Exploring the Physics of a Mass-Reduced Cube

    First of all I apologize if silly speculative discussions like this don't belong here. With that disclaimer out of the way, here's a fun thought experiment: Let's say an object, a cube that weighs 1kg rests on a rigid, level surface. And all of a sudden 99% of its mass disappears. What happens...
  28. vinamas

    Finding the Density of a Floating Cube

    Homework Statement A wooden cube is floating in a cup containing drinking water and an unidentified fluid.0.5 of the cube's volume is submerged in water and 0.4 of the cube volume is floating on the unidentified fluid find the density of the cube and the density of the unidentified...
  29. alexmahone

    MHB What Does the Branch of the Cube Root Function Mean?

    Let $f(z)=z^{1/3}$ be the branch of the cube root whose domain of definition is given by $0<\theta<2\pi$, $z\neq 0$ (i.e. the branch cut is along the ray $\theta=0$.) Find $f(-i)$. Could someone please help me understand the question? I'm not too clear on "branches" and "branch cuts".
  30. A

    Mysterious Ice Cube Tray Phenomenon

    I'm sure this is a totally amateur question, but today I got one of those big ice cube trays for 2x2x2 inch cubes. I filled it up and put it in my freezer, and about 6 hours later checked on it but the water was not frozen at all. Not even a crust on top. I put my finger in one of the squares...
  31. RaulTheUCSCSlug

    I Normalizing Constant 3D Infinite Well

    For time independent Schrodinger's equation in 3-D Where Enx,ny,nz=(nx/Lx2+ny/Ly2+nz/Lz2)(π2ħ2/2m and Ψnx,ny,nz=Asin(nxπx/Lx)sin(nyπy/Ly)sin(nzπz/Lz) How do I normalize A to get (2/L)^3/2? I don't think I understand how to normalize constants.
  32. CARNiVORE

    Net Charge within a Gaussian Cube

    Homework Statement The figure shows a closed Gaussian surface in the shape of a cube of edge length 1.80 m. It lies in a region where the electric field is given by E= (2.86x + 3.82)i + 7.18j + 8.36k N/C, with x in meters. What is the net charge contained by the cube? Homework Equations ε0...
  33. K

    Radiation Rate of 0.1m Cube Metal at 200C

    Homework Statement At what rate does a 0.1m cube of metal with emissivity e=0.75 radiate energy if it is at a temperature of 200C? Homework Equations H=AeσT^4, σ=5.67 x10^-8 The Attempt at a Solution I found the area of the cute to be A=(0.1m)^2=0.01m, and the turned 200C into 473K, but when...
  34. A

    Find the mass and side length of unknown ice cube?

    Homework Statement transfer 650 EJ (10^18 joules) into an ice cube of unknown size. the temperature of h20 increases from -10c to 20c. Given: 1) q=mc(t2-t1) 2) for phase change q=m(F) specific heat of ice (c)= 2.22x10^3 J.kg^-1.K-1 heat of fusion (f)= 3.33x10^5 J/kg specific heat of water (c)...
  35. E

    Can boiling water inside steel cube make it explode?

    Hello Lets say we have a steel cube, then fill it with water and close all the gaps very strong with welding. If we leave the cube on a stove for a lot of time, is the produced steam of the boiling water, enough to destroy and smash the steel cube?
  36. SlowThinker

    Radio Transmissions: Is It Possible in a 1x1x1m Cube?

    This should be a simple question but I'm really not sure what's the answer. Let's make a thought experiment: I have a radio transmitter and a radio receiver, operating at wavelength 10 meters. I put them in a sealed copper cube that is only 1x1x1 meter. Will the two radios be able to communicate...
  37. J

    Density: Cube of Aluminum to Copper Sphere

    Homework Statement What is the diameter of a copper sphere that has the same mass as a 9.00 cm× 9.00 cm× 9.00 cm cube of aluminum? Density of Aluminum = P(al) = 2.70g/cm3 Density of Copper = P(cu) = 8.96 g/cm3 Volume of Aluminum Cube = Vcube = 729 cm3 Homework Equations Volume of a Sphere =...
  38. anemone

    MHB Cube Root Challenge: Prove Inequality

    Prove $\sqrt[3]{43}<\sqrt[3]{9}+\sqrt[3]{3}<\sqrt[3]{44}$
  39. james_dear

    Orbit of Cube Planet: Physics Explained

    What is the physics behind a orbit a cube planet. Does the convential physics including keplars laws and circular motion still apply. Also The cube having a centre of mass posited in the middle of the cude does this mean it can be consider point mass and the same as spherical planet orbit? any...
  40. A

    What is the solution to the 12 resistor cube problem using symmetry?

    Q. It is a classical problem in current electricity .The resistor cube consists of 12 resistors, each having a value r. What is the total resistance between the two diagonally opposite corners labeled A and H on the cube? Ans. The answer to this problem begins with that due to symmetry points E...
  41. BrianKim

    Octahedron in Cube: Proving the Possibility

    I heard somewhere that the Octahedron can't exist in the Cube exactly. Is this true? Can't I prove that the octahedron in the cube? Intuitively, they seems true. But I can't sure.
  42. Z

    Stress and deformation compressed cube

    Hi, sorry for my bad english. PART A I have a cube of 10mm x 10mm x 10mm which is compressed with a stress of 0.5 Mpa on his superior face (σz=-0.6) young modulus=20Mpa, poisson coef=0.5 I have the stress tensor: [ 0 0 0] [ 0 0 0] [ 0 0 -0.6] And then, the deformation tensor is : [0.015 0 0] [...
  43. Z

    Analysing Cube Stress & Deformation in Figure A & B

    We have a cube with sides of 10mm (fig a) (in the same material than the exercice 1 (have poisson coef & young's modulus) A- figure A 1- Write the stress state and the relatives values deformations (tensor) 2- Why the sum of relatives deformation is equal to 0? B-Figure...
  44. S

    Proving Polytopes: Simplex, Cube, & Octahedron

    Homework Statement Prove that the set $$\Delta = \left\{x \in \mathbb{R}^{n+1}: \sum_{i=1}^{n+1} x_i = 1 \quad \text{and} \quad x_i \geq 0 \; \text{for any} \; i\right\}$$ is a polytope. This polytope is called an ##n##-dimensional simplex. Prove that the set $$C = \left\{x \in...
  45. S

    Electric field at the edges of a cube

    We are given a uniformly charged (non-conductor) cube. It is required to understand how the field strength along the edges relates to the field strength over the center of a face. The correct answer is apparently that the field will be weaker along the edges than over the center of a face...
  46. Kurtis McIntosh

    How Do You Calculate Net Electric Flux Through a Cube?

    Homework Statement Assume the magnitude of the electric field on each face of the cube of edge L = 1.07 m in the figure below is uniform and the directions of the fields on each face are as indicated. (Take E1 = 35.1 N/C and E2 = 25.3 N/C.) A.) Find the net electric flux through the cube. B.)...
  47. P

    Force at center of cube due to four charges of equal mag.

    Homework Statement Four charges of 2*10^-7 are placed on the corners of one face of a cube of 15 cm. A charge of -2 * 10^-7 C is placed at the center of the cube. What is the force on the charge at the center of the cube? Homework Equations F = k q_1*q_2/r^2 The Attempt at a Solution...
  48. gracy

    Electric flux calculatio in case of a cube

    Homework Statement the electric field components in the figure below are Ex=800 x^2 N/C ,Ey=Ez=0 calculate the flux through the cube a=assume 0.1 m Homework Equations The Attempt at a Solution here flux of cube =flux through ABCD =800a^2 i^.a^2 i^...
  49. Antonius

    Calculating Net Charge Inside a Cube in an Electric Field

    Homework Statement A large cube has its bottom face on the x-z plane and its back face on the x-y plane. The corners on the x-axis are at (7.93 m,0,0) and (15.9 m,0,0). The cube is immersed in an electric field pointing in the positive x-direction, and given by: E = (44.9x2 - 9.92)i, x is...
  50. I

    Did I Calculate the Force on a Superconducting Cube Correctly?

    Hi everyone, I need some help to look if I did these calculations right.Let us assume a three dimensional magnetic field: ##\vec{B}(x,y,z) = B_x(x,y,z)\hat{x} + B_y(x,y,z)\hat{y} + B_z(x,y,z)\hat{z}## The equation for the force on a superconducting particle in a magnetic field is given by...
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