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. M

    Prove two squares and a cube equal an integer

    Homework Statement Disprove or prove the statement that every positive integer is the sum of at most two squares and a cube of non-negative integers.2. The attempt at a solution I'll call the numbers that can be squares a and b. C will be the cube. The easiest way to disprove something is to...
  2. D

    Is a Point Inside a Tilted Cube?

    I'm trying to figure out if a point is in a cube that could be tilted in any direction. How would I do it? I can get anything you need for this problem. Thanks in advance.
  3. M

    3 cube roots, 4 fourth roots, and N nth-roots of -1

    My "Computational World" class is supposedly an intro to computer science without programming, but the questions are all over the place. I'm completely stuck on this question: Show expressions for: (a). 3 cube roots of -1 (b). 4 fourth roots of -1 (c). In the general case, N nth-roots of...
  4. D

    How do you calculate the total E-field for a cube with a 3D vector E-field?

    I have a cube with sides l and therefore a total volume of l^3. The E-field is ax + by + cz where a, b, and c are known constants. It says to find the total E-field. The answer is (a + b + c)*l^3. I have no idea how they get this. I tried summing up all of the sides separately bit I kept getting...
  5. R

    Flux Through a Cube: Calculate Φ & q

    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 1.3 m. (a) What is the flux through the cube if the electric field is given by E...
  6. I

    A 8.0×10^-2 kg ice cube at 0.0 degrees C is dropped into a Styrofoam cup

    Homework Statement A 8.0×10^-2 kg ice cube at 0.0 degrees C is dropped into a Styrofoam cup holding 0.35 kg of water at 12 degrees C. A) Find the final temperature of the system. Assume the cup and the surroundings can be ignored. B) Find the amount of ice (if any) remaining. C) Find...
  7. M

    Square root and cube root question

    Homework Statement why is it possible to take the cube root of a negative number and not a square root of a negative number? Homework Equations The Attempt at a Solution
  8. Z

    Factoring something with cube power?

    Homework Statement I need to find where these two intersect: x = y^3 x = 3y + 2 Homework Equations The Attempt at a Solution I set them to equate: y^3 = 3y + 2 y^3 - 3y + 2 = 0 How do I factor this??
  9. S

    What is the Electric Flux Through a Cube and How Can it be Calculated?

    Homework Statement A cube has sides of length L = 0.500 m. It is placed with one corner at the origin as shown in Fig. 23-29. The electric field is uniform and given by E = (2.50 N/C) i - (4.40 N/C) j. Find the electric flux through each of the six cube faces S1, S2, S3, S4, S5, and S6...
  10. F

    Ice cube into water/thermal equilibrium

    Homework Statement A 400 cm3 glass is filled with 100 g of ice at 0°C and 170 g of water at 25°C. Characterize the content of the glass after equilibrium has been reached. Neglect heat transfer to and from the environment. _ g (mass of water) _ g (mass of ice) _°C (equilibrium...
  11. C

    Euler's Angles for Rotating a Cube

    Homework Statement What are the Euler's angles corresponding to the rotations of a cube in \theta radians around each of its principal axes around the x: \theta=\theta \phi=\psi=0 around z:\psi=\theta=0 \phi=\theta around y:\phi=\theta=\theta \psi=-\theta is it correct...
  12. C

    Which cube has a larger moment of inertia?

    To which of the two cubes has a larger moment of inertia? I think it's the right one because We know that the minimal moment of inertia is throw the principal axes that goes throw the center of mass. in the right one , the rotation isn't throw the principal axes . there is also the following...
  13. K

    Ice cube placed in water - find final temperature

    Homework Statement A 75 gram ice cube at 0 degrees Celcius is placed in 825 grams of water at 25 degrees C. What is the final temperature of the mixture? Homework Equations What is the best formula to use in this question? The Attempt at a Solution I have attempted this problem...
  14. W

    Volume of cube with three holes

    Hello. I have been set a problem by a student. It appears to be fairly old, but I cannot find much info in the web. Here it is: A 1" cube has three holes drilled in it, each hole connecting the centres of opposite faces, thus forming a cavity in the centre joined to the surface by six holes...
  15. K

    Bouyant force on a cube floating at the surface between water and oil?

    Homework Statement A cube of 15 cm is floating at the surface between water and oil. The oil has a density of 810 kg/m3. If the cube floats so that it is 52% in water and 48% in the oil, what is the mass of the cube and what is the buoyant force on the cube? Homework Equations...
  16. D

    Find Miller Indexes of SC Cube Planes: FAN, KFA, HAN

    for the following SC cube, find the miller indexes for the planes: FAN KFA HAN http://lh6.ggpht.com/_H4Iz7SmBrbk/SvhiU8OeicI/AAAAAAAAB8M/o8QPR2ht2gA/Capture.JPG what i leared to do was find the points that the plane intercepts the x,y,z axis, i chose axes such that x+ is pointing...
  17. D

    How can i keep an ce cube from melting?

    what method can be used to keep a regular 2cmx2cmx2cm ice-cube from freezing. i need to find a way to keep an ice cube solid for 10 hours after taking it out of the freezer without using electricity or by adding more ice etc. the question comes from my chemistry lecturer so i would expect it to...
  18. G

    Cycle decompositions of the rigid motions of the cube

    Homework Statement Write down cycle decompositions of all 24 of the rigid motions of the cube by regarding each rigid motion as a permutation of the 6 faces. Then, this is a subgroup of S_{6}, called S_{CUBE}. Prove or disprove that S_{CUBE} is a subgroup of A_{6} Homework Equations...
  19. L

    Gauss' Law with a cube

    Homework Statement Non conducting solid cube with a uniform charge distribution. Why is it impossible, or extremely difficult to calculate the field using a larger cube as the gaussian, what about with a sphere as the gaussian? Homework Equations gauss' law The Attempt at a...
  20. P

    Linear algebra - side of a cube is an integer?

    Homework Statement A cube of sides a*a*a is in 3 dimensional space. All eight of its corners have integer coordinates. Prove that a is an integer. Homework Equations - The Attempt at a Solution First, I considered three corners of the cube p, q and r, with these, two vectors...
  21. Q

    How Does Flux Distribute in a Gaussian Cube with a Corner Charge?

    Homework Statement A particle charge of q is placed at one corner of a Gaussian cube. What multiple of q/\epsilon_0 gives the flux though each cube face not making up that corner? The solution is amazing - stack up eight cubes around the corner and find the flux through each individual cube...
  22. P

    Max Volume of Cube from 1000 cm^2 Sheet

    A sheet of material 1000 cm^2 is given to you to construct a box/cube with no lid. What is the maximum volume of the cube that can be created in cm^3?
  23. G

    Flux of a Point Charge Inside a Cube: Part A & B

    Homework Statement A point charge of magnitude q is at the center of a cube with sides of length L. Part A What is the electric flux Phi through each of the six faces of the cube? Part B What would be the flux \phithrough a face of the cube if its sides were of length L1...
  24. fluidistic

    Understanding Purcell's Cube: Attraction to Mass Center?

    In the Spanish second edition of "Electricity and Magnetism", Berkeley Physics Course, volume II, page 27, Purcell states that a cube with a perfectly constant density does not attract external bodies as if its mass was concentrated in its geometrical center. However he does not say how does...
  25. W

    You have a 3x3x3 cube, built with 1x1x1 bricks (27 bricks in total).

    You have a 3x3x3 cube, built with 1x1x1 bricks (27 bricks in total). You remove two diagonally opposite bricks (long diagonals). Can you build the remaining figure from 2xx1x1 bricks?
  26. N

    What happens when I put cube and square doubles in a matrix?

    I think I've managed to construct a symmetric set of functions, that let's a x, x^2, x^3\; double an algebraic number. I have a series that goes {6,9},{27,54} already. If I set x = 3, then I replace these terms with \; \{ 2x, x^2 \} ; \{ x^3, 2x^3 \} I have the series and a symmetric set...
  27. DocZaius

    Volume of a Cube: Integrating s3 vs. s^3/3

    Note this is not a homework assignment. I was generally learning about integrating volumes and thought that after being able to integrate the volume of a cylinder \int^{L}_{0}\pi r^{2} dL That I maybe could integrate the volume of a cube in a simple way: \int^{s}_{0}s^{2} ds Yet that results...
  28. K

    What is the size and direction of the force on each segment in this gif?

    i need to figure out the size and direction of the force on each segment http://i32.tinypic.com/1075g8g.gif in cd segment there is a 45 degree between the electricity and magnetic field so i need to have size 40*sin 45 why they write only 40 ??
  29. E

    An ice cube floating in water, what is the volume of the part under water?

    The Problem Hi, I just got this question in a physics class that I am taking, I have been looking at it for about 30 minutes and can't seem to crack it, probably doesn't help that I'm learning it in another language but anyways. A Ice cube of temperature 0 degress Celsius is floating on water...
  30. P

    Point inside a cube of irregular dimesnion

    hi, Is there any way, to find a point whether it lies inside a irregular cube. other than finding volume. where cube can be rotated in any direction.
  31. M

    Is \sqrt[3]{2} Irrational and Cannot be Represented by Rational Numbers?

    Hey guys. I forget where I found this problem but it goes as follows: Prove that \sqrt[3]{2} cannot be represented in the form p+q\sqrt{r} where p,q, and r are rational numbers. It is easy to show that \sqrt[3]{2} is irrational, so it cannot be put in the form m/n, where m and n are...
  32. W

    How Do You Calculate Cube Roots of Complex Numbers in Modulus Argument Form?

    can someone help me solve this question as fasd as possible?? im really headache wif it... thx~~ determine the 3 cube roots of 3-i over 3+i giving the result in modulus argument form,express the principal root in the form a+Jb
  33. F

    Cube collision (with a pivot) and Angular momentum

    Hi everybody some help needed here! A cube, mass M move with v0 collide with small object "fixed" to the surface in Point P that make it pivot over its side So far I think I understand: During the impact there is no conservation of KE L Angular Momentum : there is an unknown force F...
  34. B

    How to Determine the Depth of an Ice Cube Floating in Water?

    Homework Statement A cube of ice whose edge measures 20.8 mm is floating in a glass of ice-cold water with one of its faces parallel to the water's surface. How far below the water surface is the bottom face of the block? Homework Equations P=F/A, P2-P1=\rhogh The Attempt at a...
  35. R

    Calculating Surface Integral with Stokes' Theorem on a Cube?

    Homework Statement I have to use stokes' theorem and calculate the surface integral, where the function F = <xy,2yz,3zx> and the surface is the cube bounded by the points (2,0,0), (0,2,0),(0,0,2),(0,2,2),(2,0,2),(2,2,0),(2,2,2). The back side of the cube is open. [/B] Homework...
  36. C

    What is the tension in the string connecting a cork and a cube in water?

    One end of a light thin string is attached to the bottom of a 3.7 g, 42 cm3 cork. The other end is attached to a 58 g cube. The arrangement is placed in water and it is found that with 82% of the cork submerged the cube is held in equilibrium. What is the density of the cube in g/cm3? I need...
  37. M

    Determine the ice cube temp change

    Trying to beat the heat of the last summer, a physics student went to the local toy store and purchased a plastic child's swimming pool. Upon returning home, she filled it with 200 liters of water at 25oC. Realizing that the water would probably not be cool enough, she threw ice cubes from her...
  38. K

    Miller indices of a plane in a simple cube

    I am trying to get a hang of miller indices and doing some practice. So here it is : What would be the miller indices of the plane containing the x-axis and equally inclined to y and z axes? (I have uploaded the diagram and highlighted the plane to clarify) Attempts : I first try to...
  39. 2

    Determine the net charge contained within the cube

    Homework Statement At each point on the surface of the cube shown in the figure, the electric field is parallel to the z axis. The length of each edge of the cube is 3.7 m. On the top face of the cube = -40 N/C, and on the bottom face of the cube = +10 N/C. Determine the net charge...
  40. Ed Aboud

    Flux through each face on a cube

    Homework Statement A point charge q is placed at one corner of a cube of edge a. What is the flux through each of the cube faces? Homework Equations The Attempt at a Solution I drew a diagram of the situation. I'm pretty sure that I should use Gauss' Law and some symmetry...
  41. S

    Flux of Vector Field F out of Cube: 1

    Homework Statement What is the flux of vector field F = xi + zj out of the cube that has corners in (0,0,0),(1,0,0),(0,1,0),(0,0,1),(1,1,0),(1,0,1),(0,1,1),(1,1,1). The Attempt at a Solution Is it 1? Divergence = del dod F = 1 Triple integral of divergence= SSS 1 dx dy dz each from 0...
  42. K

    A question on finding the resistance from a 3D cube

    Homework Statement Find the resistance between the points a and b for the resistor network shown. http://s5.tinypic.com/1073kvd.jpg The Attempt at a Solution I changed to 3D cube into a 1D square and each side of the square contains 3r because each side of the cube contains an r(for...
  43. D

    Finding Electric Flux of Cube with E Field

    given a cube,each side with a lenth of A, placed at with its back left hand bottom corner at (0,0,0). find the electric flux passing through the sides if the electric field is a) E=(-3x)i + (2y)j + (4z)k b) E=(sin(pi*x/A)i + cos(pi*y/2A)j for a) since the area of each side is A2...
  44. M

    Divide a large cube into 125 smaller cubes of equal size?

    Could somebody please tell me how can one divide a large cube into 125 smaller cubes of equal size? I can very well understand i can divide a large cube into 225 smaller cubes because 15*15=225. I just HAVE NO ideas. You?
  45. S

    How Does an Impulse Affect the Motion of a Cube?

    I'd be grateful if someone could help me with the problem below: A free-floating uniform cube with sides of length 2 is at rest, aligned with the coordinate axes, when it is subjected to an impulse along one edge of 3m, where m is its mass. What is the effect on its motion? (Its inertia...
  46. C

    How far above the water is the top surface of the cube?

    A cube of wood measures 0.55 m on each side and has a mass of 133.1 kg. How far above the water is the top surface of the cube? Can someone help me out with this one
  47. L

    Flux through a Cube - Why would flux be zero?

    Homework Statement This is a three part problem. I have the first and third part down but I'm just wondering about the second part which is multiple choice. A cube has one corner at the origin and the opposite corner at the point (L,L,L). The sides of the cube are parallel to the...
  48. F

    Proving a Factor of Complex Cube Root of 1 in x^3 + y^3 + z^3 - 3xyz Equation

    Homework Statement If w is a complex cube root of 1, prove that x + wy + w^2z is a factor of x^3+ y^3 + z^3 - 3xyz, and hence factorise the equation completely. Homework Equations Complex cube root of 1 = -1/2 +/- 3^1/2/2 i The Attempt at a Solution Erm, I feel way over my head...
  49. O

    Calculating Electric Flux Through a Cube with a Non-Uniform Electric Field

    Homework Statement Homework Equations E * A The Attempt at a Solution I need to find the electric flux through each face. I am a bit confused. I believe the flux through sides 3 and 1 are zero because those sides are parallel to the electric field. The whole flux through the cube should be...
  50. 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...
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