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

    Cube Electric Field: Are Intersections Uniformly Distributed?

    Homework Statement A positive charge is located at the center of a cube. Are the intersections of the field lines with a side of the box uniformly distributed across that side? Explain The Attempt at a Solution I'm trying to picture this in my head and I'm getting stuck. I know the field...
  2. P

    Thermodynamics ice cube question

    Homework Statement How much energy is required to change a 40.0 g ice cube from ice at -8.0°C to steam at 108°C? Homework Equations q=mct The Attempt at a Solution i remember one of our TAs going over something like this a long time ago..I think i have to like add up all the...
  3. B

    Hollow cube - moment of inertia

    Homework Statement How to calculate moment of inertia of hollow cube. Homework Equations The Attempt at a Solution I guess that subtracting the moment of inertia of the inner cube from the moment of inertia of the outer cube is wrong. Even it is close to solution, what mass to put in...
  4. Saladsamurai

    Check Divergence Theorem on Unit Cube

    Homework Statement Check the Divergence Theorem \int_V(\nabla\cdot\bold{v})\,d\tau=\oint_S\bold{v}\cdot d\bold{a} using the function \bold{v}=<y^2, 2xy+z^2, 2yz> and the unit cube below. Now when I calculate the divergence I get (\nabla\cdot\bold{v})=2y+2x+2y but Griffith's...
  5. J

    Flux through one side of a cube

    Homework Statement A charge q sits at the back corner of a cube. What is the flux of E through the opposite (front)side? Homework Equations Flux=q/ε_0 The Attempt at a Solution As the flux through the whole cube must be q/ε_0, I thought that for one side it would just be...
  6. M

    Heat Transfer black-body cube Problem

    How many days does it take for a perfect black-body cube (0.0100 m on a side, 30 degrees C) to radiate the same amount of energy that a one-hundred-watt light bulb uses in one hour? If someone could point me in the right direction with how to go about solving this problem i would greatly...
  7. H

    This will work for all six sides of the cube.

    Homework Statement Calculate the total flux of vectorF(x,y,z)=8x^2y i + 6yz^2 j + y^3z k outward through the cube whose verticies are(0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1),(1,1,1), (0,1,1). Homework Equations \int\int \widehat{}F \bullet (-partial z/dx i -partial z/dy j +...
  8. M

    Flux of F over the surface of a cube

    Homework Statement Find the flux of F over the surface of the cube with vertices ( \pm 1, \pm 1, \pm 1) using the outer normal. F(x,y,z)=(x+y)i+zj+xzk Homework Equations Flux of F over S is \iint F \cdot n dS The Attempt at a Solution I think the normal should be 1 in the...
  9. D

    Nxn rubik's cube - how many orientations?

    I'm sitting here with my new 5x5x5 rubik's cube, and I was just wondering how many possible orientations there were. I THOUGHT: -Each corner has 3 orientations and 8 positions -Each middle side has 2 orientations and 12 positions -Each outer side has 2 orientations and 24 positions -etc etc...
  10. M

    How High to Release a Granite Cube to Achieve Specific Speed in a Steel Cube?

    Homework Statement a 100g granite cube slides down a 40 degree frctionless ramp. at the bottom, just as it exits onto a horizontal table, it collides with a 200g steel cube at rest. how high above the table should the granite cube be released to give the stell cube a speed of 150cm/s...
  11. N

    Freezing Water: 100cm³ of Water vs. Ice Cube

    1. The diagram shows a strip of paper tape that has been pulled under a vibrating arm by an object moving at constant speed. The arm is vibrating regularly, making 50 dots per second. What was the speed of the object? A. 2.0cm/s B. 5.0cm/s C. 100cm/s D. 200cm/s Completely clueless...
  12. D

    Derivative of the volume of a cube

    I am asked to find the second derivative of the volume of a cube with respect to the length of a side. would my initial f(x)=x3/x ?? than just follow with the quotient rule to get f(2)(x)?
  13. H

    How to Factor a Cube: Exploring Denominators and Graphs for Asymptotes and Holes

    Homework Statement I am trying to find out when the denominator of this equation is zero so I can tell when the graph has asymptotes or holes. For squares I factor such as x2+2x-15 = (x+5) (x-3). How do I do that with a cube? Homework Equations (x-5) (x+3) X3-5x2+x-5
  14. C

    Finding Charge on a Cube Corner

    Homework Statement Given a cube with equal charges on all corners save one, find the charge on the origin. http://img79.imageshack.us/img79/4968/cubekg7.jpg Homework Equations F = kQ1Q2The Attempt at a Solution My current idea is splitting up the magnitude of all charges on the origin into...
  15. I

    Solving Flux of Electric Field through a Cube of Side L = 2m

    Homework Statement A cube of side L = 2m is centered at the origin, with the coordinate axes perpendicular to its faces. Find the flux of the electric field E = (15N/C)i + (27N/C)j + (39N/C)k through each face of the cube Homework Equations phi total = (E * n) delta A The Attempt...
  16. S

    Calculating Angle Between Cube Ribs

    hello , How are you all? look at this question what the magnitude of the angle that between two ribs from the heads of the cube to its center ? I attempted by using cosine law [look at the pecture in attachment] but, Hwo to apply this law on the cube (3D)? any one help me >>and thank you...
  17. A

    Finding Flux of Vector Field F Through Cube S

    Homework Statement I need to find the flux of the vector field F through S (in the pic), when S represent the edges of a cube. My question is, how do I find N (normal)? Do I need to split the curb and to find the flux through each face?Homework Equations The Attempt at a Solution
  18. B

    Entropy of system with ice cube in lake

    An ice cube of 10g -10°C is placed in a lake that is 15°C.Calcule the variation of entropy of the system when the ice cube to reach the thermal balance with the lake. The specific heat of the lake is 0,50cal/g°C.:biggrin:
  19. S

    What are the bound charges of a polarized dielectric cube with no free charges?

    Homework Statement Consider a permanently polarized dielectric cube with the origin of the coordinates at the center of the cube. The cube has a side of length a. The permanent polarization of the dielectric is \vec{P} = c \vec{r}. The vector \vec{r} is the radius vector from the origin of the...
  20. B

    Angle between diagonals of a cube

    Homework Statement Find the acute angle between two diagonals of a cube. Homework Equations N/A The Attempt at a Solution I know that the length of a diagonal of a cube whose side lengths are each one is sqrt(3), so I think it has something to do with that. Other than that, I'm...
  21. S

    ANGAMWhat is the Integral of Cube Root of Cot(x)?

    Hi, I just registered on to the forums, and I have to say it is a very good job. I am currently a senior at High School and aiming for an Engineering Course. While solving some integrals, I got stuck upon this one, and even after a lot of attempt, my friends and I could not solve it. Hence I...
  22. J

    Using a differential to approximate a cube root

    Homework Statement Use the differential dy or L to approximate cubed root 1.03 Homework Equations L(x)= f(a) +f'(a)(x-a) The Attempt at a Solution I have no clue how to start so that would be the most help, do i just find the derivative of cubed root 1.03 first?
  23. C

    (Not a text brainteaser) Speed Solving the Rubik's Cube

    Who else does it? I can solve the cube in under 30 seconds, but I average around 36 seconds. If anyone else does this, please reply. I want to see how many people are better than me. ~Nick
  24. H

    Ice Cube Floating: Help with Bouyancy Question!

    Hi! I'm new to the forums and this is the first that I'm posting something :D! I have a quick question from my textbook that I got wrong. Can someone please help me out! Thanks in advance! Question: An ice cube is floating in a glass of water that is filled entirely to the brim. When the...
  25. K

    Equilibrium problem involving cube root

    Homework Statement The reaction 2Fe3+ + Ni(s) = 2Fe2+ + Ni2+ has equilibrium constant K = 1.5E34. What is the concentration of Fe3+ at equilibrium if a lot of Ni(s) is added to a 0.1 M solution of Fe3+ that initially contains no Fe2+? The Attempt at a Solution K = 4x3/(0.1-2x)2 My...
  26. C

    Express the surface area of a cube

    Homework Statement Express the surface area of a cube as a function of its volume. Homework Equations Cubic Volume=Length x Width x Height (V=Length of side^3) Cubic Surface Area= (Length of side^2)x6 The Attempt at a Solution f(V)=(X^3/X) x 6...sorry, I don't know if I'm on the...
  27. D

    What is the flux through (a) each cube face

    A point particle with charge q is placed at a corner of a cube of edge a . What is the flux through (a) each cube face forming that corner and (b) each of the other cube faces? I tried modelling the problem by positioning the charge such that it is at point (0,0,0) in the x-y-z space. The...
  28. E

    The volume of a cube and a cylinder.

    I was wondering if the formulas for the volume of, for instance, a cube and a cylinder are definitions or if they can be proved. Does anybody know :)?
  29. M

    Solving Heat Transfer in an Aluminum Cube: Find Temperature After t Seconds

    Suppose that I have an aluminum cube with side lengths 10 cm. Suppose that I uniformly and continuously apply a temperature of 60 degrees celcius to one of its sides. The medium surroudning it is air with a temperature of 27 degrees celcius. After t seconds, what is the temperature of the...
  30. B

    What Happens to the Cube's Velocity After Colliding with a Pivoting Rod?

    Homework Statement A cube of mass m slides without friction at a speed vo. It undergoes a perfectly elastic collision with the bottom tip of a rod length d and mass 2m. The rod is pivoted about a frictionless axle through its center, and initially it hangs straight down and is at rest. What...
  31. E

    Volume of a cube versus side length

    Show that the rate of change of the volume of a cube with respect to its edge length is equal to half the surface area of a cube. I know that surface area= 6l^2(because of the six faces) I know that volume is l^3. How do I relate volume then to edge length
  32. humanino

    Ants Walking Around a Cube: Find Number of Paths of Length N

    Hi, An ant is walking along the edges of a unit cube. The goal is to find the number of paths of length N from one vertex to another. Any path is allowed along the edges, back and forth any number of times.
  33. B

    Conservation of Energy Ice Cube Problem

    Homework Statement A very slippery ice cube slides in a vertical plane around the inside of a smooth, 20 cm diameter horizontal pipe. The ice cube's speed at the bottom of the circle is 3 m/s. a) What is the ice cube's speed at the top? b) Find an algebraic expression for the ice cube's...
  34. M

    Electric flux through one face of the cube.

    A point charge Q = 5.00 µC is located at the center of a cube of side L= 0.120 m. In addition, six other identical point charges having q = -0.50 µC are positioned symmetrically around Q, as shown in Figure P24.19. Determine the electric flux through one face of the cube.
  35. A

    Units of Computing Power: How Much for a 1cm^3 Cube?

    I often hear about how solving some problem would require a computer "the size of the known universe", or something like that. Is there a "unit" of computing power? How many units of this power would say a 1cm^3 cube of hot gas have? In other words assuming you wanted to simulate the actual...
  36. B

    Melting Ice Cube: Time Needed for 3-Ton Ice Cube with Golden Bars

    Help...melting ice cube. Homework Statement How much time is needed for an ice cube ((1.5x1.5x1.5)m, 3tons of mass with two golden bars within an ice cube to melt. Average temerature of the month is 6.2 ˙C Thank you very much!
  37. N

    Building a Slingshot in a 1m Cube - Grade 12 Physics Project

    Well... I am in grade 12 Physics and we were asked to make a Slingshot to fit within a 1 meter cube. If anyone has any ideas or know any websites with plans to making one.. it will be very helpful Thank you.
  38. E

    LaTeX How do you get a cube, fourth, fifth root in latex?

    [SOLVED] latex question How do you get a cube, fourth, fifth root in latex? I mean how do you get a little 3 to appear in the upper left next to the square root sign?
  39. T

    Calaculate Mass of Cube submerged in oil and water

    [SOLVED] Calaculate Mass of Cube submerged in oil and water Homework Statement A cube is submerged in water and oil the oil is on top, and forms a layer 10cm thick. the water is underneath and forms another layer 10cm thick. the cube has sides of 10.2cm, and has 2.3cm below the oil water...
  40. H

    Mastering the Rubik's Cube: Advanced Strategies and Speed Cubing Techniques

    Some tutorials that helped me learn the Rubik's Cube: http://sciencehack.com/pages/page015 I'd like more complex ones though with a focus on strategy and speed cubing. Any ideas?
  41. S

    Exploring the Unit Cube in [tex]\ R^{n}[/itex]

    I'm having trouble visualizing [tex]\ R^{4}[/itex](a domain of reals in four dimensions). 1. Describe a procedure in given 3 vectors, finds a fourth vector perpendicular to those three. Explain why we can use it in analogous fashion to the normal vector to a plane in [tex]\ R^{3}[/itex]. Here...
  42. Z

    Solving the Gaussian Cube Question: Understanding E = 7.35i - 5.63(y2 + 9.74)j

    http://img255.imageshack.us/img255/8083/47252155dr7.jpg Okay I totally don't understand this problem at all. There is an example in the book also, but I just don't understand how to do it. Like the whole concept of how the E is written. I don't understand what this means: E = 7.35i - 5.63(y2...
  43. D

    Solving Physics Lab Cube Sliding Problem

    In a physics lab, a small cube slides down a frictionless incline as shown, and collides at the bottom (where it is now moving horizontally) with a cube that is only one-half its mass. If the incline is 30 CM high and the table is 90 CM off the floor. where does each cube land? the teacher...
  44. J

    What is the electric flux through the top surface of the cube?

    Homework Statement A 3 nC point charge is at the center of 5 m x 5 m x 5 m cube. What is the electric flux through the top surface of the cube? Homework Equations E=kq/r^2 φ = E.A The Attempt at a Solution E = (8.99*109)(3*10-9) / 2.52 = 4.3152 N/C φ = E.A = (4.3152)(5*5) =...
  45. B

    Flux of a Cube with a Corner Charge

    Homework Statement A point charge is placed at a corner of a cube. What is the net flux through all faces of the cube? Homework Equations The Attempt at a Solution \phi = \frac{q}{\epsilon_0} or perhaps \phi = \frac{q}{8\epsilon_0} The latter solution is based on the...
  46. N

    Exploring the Weight of a Submerged Cube: Can You Determine its Volume or Mass?

    No question that it's simple, but for some reason I can't fully understand this. I stumbled upon this problem asking "If we put a glass of water on a digital weighing scale and we reset the scale to zero, after which we submerge a cube of an unknown material in the water attached to a string...
  47. C

    Why does a hot or warm ice cube tray freeze quicker than one at 33*F?

    I have the answer, it is because the refrigerator is not in freeizng mode when the cold ice cube tray is placed inside. When the warm tray of water is placed inside then the temperature lowers considerably and the thermostat switches the freezer into freezer mode. A common complication I...
  48. B

    Volume of a cube moving relativisticly fast

    The volume of a cube is Vo when it is at rest. Show that the volume of the cube when it is moving relativisticly fast is given by relativistic velocity = rest velocity*square root of (1-(v/c)squared)
  49. R

    Calculating Depth of Water in Floating Cube

    [b]1. A hollow cubical box is .30 m. This box is floating in a lake 1/3 of its height beneath the surface. The walls of the box have neglibe thickness. Water is poured into box. what is the depth of the water in the box at the instant the box begins to sink? pwater= 1000kg/m3 Fb= Pfluid G V...
  50. W

    Are all configurations of a Rubik's cube solvable?

    Obviously I am not speaking of an already solved Rubik's cube which has gone under a series of changes, since undoing every change backwards constitutes itself in a solution. My question is whether or not all configurations are solvable per se, that is if the distribution of the colored squares...
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