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. S

    How Does Rotational Motion Affect a Cube and Pulley System?

    A cube of mass M = 500 g and side length 30 mm is free to spin on an axis through the center of one face. A massless pulley on this axis has a diameter of 2r = 10 mm. A weight of m = 50 g is hung from a string wrapped around the pulley. The assembly is released from rest. (a) Find the time...
  2. P

    Find the length of a side of a cube

    trying to figure this out, but am confused on the steps please help thank you The volume of a cube is given by V = s3, where s is the length of a side. Find the length of a side of a cube if the volume is 800 cm3. Round the answer to three decimal places.
  3. Saladsamurai

    Cube suspended in liquid - find tension

    a cube with edge length L=.600m and mass 450kg is suspended by a rope in an open tank of liquid of density 1030 kg/m^3. The top of the cube is L/2 deep in the tank. Find the tension in the rope. Vol=.600^3=.216 Area of top side of cube=.6^2=.36 \sum F=0 \Rightarrow...
  4. F

    Partitioning a Cube into Unequal Size Cubes: Can it be Done?

    Can you describe any partition of a cube into smaller cubes that are not the same size? (I know a few answers to this one...) It is easy to think of 8 identical cubes being combined to make one big cube. But, if the cubes don't have to be the same size: is there another way to do it? (I think...
  5. C

    What is the Zero Density Cube?

    I may be posting this in the wrong section: A while ago I was reading a collection of articles on Wikipedia and I stumbled upon this article that was pretty interesting. It was about a cube, on each face of the cube a small cube is cut out. It is done many more times. The next thing I...
  6. C

    Related rates and cube with a sphere inside of it

    I was pondering a question today. If you have a cube with a sphere inside of it, and the sphere is growing at 2 m/s. The cube itself is expanding at 1 m/s. If the cube is 5 x 5 x 5, and the sphere has a radius of 2. Is it possible to calculate when the sphere and the cube will be expanding...
  7. C

    Electric flux through gaussian cube

    Homework Statement I have a cube with four faces parallel to the field and two perpendicular. The field is non uniform, given by E = 3 + 2x^2 in the +x direction. The Attempt at a Solution So I get \phi = \int \vec{E} \cdot d\vec{A} = \int EdA = A \int E = A \int (3+2x^2) But how do I...
  8. T

    Proving that cube root 7 is irrational

    Hi guys, How would you prove that \sqrt[3]{7} is irrational without using the unique factorization thrm? I tried proving that \sqrt[3]{7} is rational but it didn't seem to get me anywhere... Thanks EDIT: Looks like I posted this in the wrong forum.
  9. B

    Find the zeros: Includes a cube

    Homework Statement Find the zeros of the function algebraically. Homework Equations f(x) = 4x^3 - 24x^2 - x + 6The Attempt at a Solution If all quantities had an x in them, I'd just factor out and x, and treat it as a quadratic. But that freaking 6 is ruining my plan and I'm stuck.
  10. M

    How Many Permutations Can a 1000x1000x1000 and 5-Dimensional Rubik's Cube Have?

    Rubik's cube permutations I suck with really big numbers, so that's where you guys come in :) I basically want to know the number of permutations a 1000x1000x1000 Rubik's cube has, as well as a 5x5x5x5x5 Rubik's cube. Yes, a 5-dimensional one. I've been reading these a formula's, and...
  11. Math Jeans

    The time cube: this guy is for real

    Some of my friends showed me a website where it is just one person ranting about this thing called a "Time Cube". He apparently claims that if we don't believe in the Time Cube, we will all result to cannibalism. This person is real, and if you watch an interview with him he is way to old to be...
  12. P

    How Does Gauss's Law Apply to the Flux Through a Cube Near a Charged Sphere?

    I have the homework problem below with which I'm totally stumped. Can anyone out there help me out? A small cube of volume 9.0 cm^3 is 0.30 cm from a metal sphere that has charge 3.00 coulombs. If the cube is empty, what is the total flux through it?
  13. C

    What is the height of a 91 lbs. gold cube?

    Homework Statement Determine the height of a 91 lbs. gold cube. Homework Equations I'm not really sure which equations are relevant here... this is an Honors Physics problem for my girlfriend, but she asked me to attempt and I'm in Physics. Anyways, I thought of and only found a few I...
  14. D

    Finding Square & Cube Roots by Hand

    Hello friends, I am studying in 10th class. Actually I have a question and I’m unable to solve this question. My question is: How can we find the square root of a number by hand? How about cube roots? If anybody can solve my question I will grateful. Thanks in advance!
  15. E

    Potential Inside Cube: What Is the Center's Potential?

    A cube has 5 sides grounded, and an insulated sixth side at potential x. What is the potential at the center of the cube? The solution states that the potential at the center must be a linear combination of the potentials of the six sides. Why is that? Thanks, EFuzzy
  16. J

    Why do ice cubes form strange icicles on top when frozen?

    So, I've noticed that when I freeze ice cubes these strange icicles appear on the top of the ice. I took a picture, included as an attachment. Not really sure how something like this forms. Please no speculation.
  17. W

    Can a cube be cut in 27 smaller cubes in less than 6 cuts?

    Prove or disprove that it is possible.
  18. S

    Troubleshooting Flux Out of a Cube: Evaluating a Double Integral

    I am trying to work through some examples we have been given on flux out of a cube but am having difficulty in seeing how one one line of the answer becomes the next. The question is analysing the flux out of a cube by looking at each side individually and working out the surface integrals...
  19. C

    How Does Powder React When Squeezed Inside a Cube?

    If I have cube with top side opened with powder in it an i start pushing two sides of cube together will powder fall out of cube the same as with water or other liquid?
  20. B

    Calculating Heat Required for Ice Cube Transformation

    How much heat is required to change a 46.6 g ice cube from ice at -12.5°C to water at 53°C? (if necessary, use cice=2090 J/kg°C and csteam= 2010 J/kg°C) then i used Q=cmt and Q=mL Q=(2090)(.0466)(12.5)=1217.425J Q=(.0466)(33.5E4)=15611J Q=(2010)(.0466)(53)=4964.298J then when i add...
  21. I

    Net Charge of Cube: -2385075 uC

    Homework Statement At each point on the surface of a cube the electric field is parallel to the z axis. The length of each edge of the cube is 3.5 m. On the top face of the cube the electric field is in the negative z direction and has a magnitude of 37 N/C magnitude. On the bottom face of...
  22. M

    How Fast Does the Diagonal of a Cube Change with Its Side Length?

    Homework Statement The side of a cube increases at 1 cm / s. How fast is the diagonal of the cube changing when the side is 1 cm? Homework Equations Involves: a^2+b^2=c^2 Implicit Differentiation Derivation The Attempt at a Solution I'm attempting to find the diagonal of the cube...
  23. N

    How Does Melting Ice Affect System Displacement in a Gravity-Free Environment?

    Homework Statement Consider a gravity free hall in which a tray of mass M,carrying a cubical ice block of mass m and edge L,is at rest in the middle.If the ice melts,what would be the displacement of the system? Homework Equations The Attempt at a Solution I think it has to do...
  24. C

    'Euler criterion' for cube roots?

    I am trying to derive a version of Euler's criterion for the existence of cube roots modulo p, prime. So far, I have split the primes up into two cases: For p = 3k+2, every a(mod p) has a cube root. For p = 3k+1, I don't know which a it is true for, but I did a few examples and noticed...
  25. K

    How Can We Model and Simplify the Melting of an Ice Cube?

    Hi everyone, I am new to this forum. I am taking an undergraduate thermodynamics course and got stumped by this problem. I found this forum and figured that someone here would be able to help me with this! :-p Homework Statement Develop a model for melting of an ice cube. What assumptions...
  26. H

    Solving a Rubik's Cube: Tips & Tricks

    Just an interesting question but has anybody here ever solved a Rubik's cube before? I need some serious help with solving one and it is driving me nuts! Anyone have some good tips? Thanks!
  27. CarlB

    Fermion Cube: Standard Model Lagrangian & Preon Model

    An elegant way of writing the standard model Lagrangian. The paper is titled "Standard Model Lagrangian" and is on this site: http://federation.g3z.com/Physics/ This appears to fit well with my preon model of the fermions; and helps fill in how one connects up the gauge bosons in that sort...
  28. J

    An Ice Cube is Added to a Thermos of Coffee

    Homework Statement An insulated Thermos contains 110 cm3 of hot coffee at 87.0°C. You put in a 15.0 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? Treat the coffee as though it were pure water and neglect...
  29. S

    Calculating Electric Flux Through a Cube

    Electric Flux of a cube Homework Statement A point charge of magnitude 9.10 nC is at the center of a cube with sides of length 0.685 m. What is the electric flux through each of the six faces of the cube? What would be the flux Phi_1 through a face of the cube if its sides were of...
  30. S

    Calculating Temperature Change with Ice Cube in Coffee

    I have a question involving putting an ice cube in a thermos of coffee. I used c_{ice}m_{ice}(T_f-T_i) + c_{coffee}m_{coffee}(T_f-T_i)=0. Is this right? If so wouldn't the temperatures of the ice remain constant until it is all gone?It says that the ice is at 0'C.
  31. J

    Calculating Electric Flux of a Cube with Charges

    Homework Statement A cube has a charge Q at its center and has 6 charges q placed symetrically around the central charge. Each one is placed the same distance from the central charge down respective axises which are perpendicular to the planes of the cube which they pass through the center of...
  32. C

    Is there a number that is exactly one more than its cube?

    is there a number that is exactly one more than its cube?
  33. M

    What is the rotational inertia of a cube when rotated about an edge?

    Does anyone know what the rotational inertia of a cube of uniform density is when it is rotated about an edge? Any help is appreciated!
  34. kreil

    How Much of a Glass Cube's Surface Must Be Covered to Hide a Central Spot?

    Homework Statement A glass cube has a small spot at its center. What parts of the cube face must be covered to prevent the spot from being seen, no matter what the direction of viewing? What fraction of the cube face must be covered? Assume a cube edge of 1 cm and a refractive index of 1.50...
  35. F

    How can I make Stepmania read serial data from a game cube to USB adapter?

    ok i wasnt sure which forum to place this in so I am putting it here now. I am currently trying to help my boyfriend figure out something. his project is to design and build a game cube to usb adapter that will work with stepmania (a dance dance revolution simulator that you can download for...
  36. F

    Game cube to usb adapter advice

    I am currently trying to help my boyfriend figure out something. his project is to design and build a game cube to usb adapter that will work with stepmania (a dance dance revolution simulator that you can download for free online). he has already correctly mapped out the buttons in his code...
  37. F

    Calculating Energy Needed to Melt an Ice Cube

    Homework Statement How much energy is necessary to completely melt an ice cube of mass 360.6grams that is initially at a temp of -25.2 degrees celsius. Homework Equations im thinkin i should use specific heat equation? is that right? c=Q/m(change of temp) 2090=Q/.36069(25.2) The...
  38. R

    Small cube/large cube sliding problem with friction quickly :/

    (I know this type of problem has been discussed on here before, but I still don't understand what to do next) The attached drawing shows a large cube (mass=55kg) being accelerated across a horizontal frictionless surface by a horizontal force P. A small cube (mass=4.5kg) is in contact with...
  39. F

    What is the final temperature if only one ice cube is used?

    Two 60 g ice cubes are dropped into 270 g of water in a thermally insulated container. If the water is initially at 25°C, and the ice comes directly from a freezer at -15°C What is the final temperature if only one ice cube is used? I have no idea where to begin...my teacher didn't give us...
  40. murshid_islam

    Cube roots of a complex number

    hi, is there any way to find the cube roots of a complex number WITHOUT converting it into the polar form? i am asking this because we can find the square root of a complex number without converting it. i was just wondering whether there is such a method for finding cube roots too. i was...
  41. P

    Exploring Rotations in a Cube: Geometric Insights and Examples

    Geometrically, how do rotations in a cube look? i.e rotate through 180 degrees about the line joining midpoints of opposite edges, how does it look? Are the rotations the different ways of getting from one vertex to the opposite vertex in the cube (where opposite is defined by the line...
  42. E

    Find Total Capacitance of Cube w/12 4.71pF Capacitors

    If I have a cube made out of capacitors, that's one capacitor for everyside for a total of 12 capacitors. Each capacitor is C=4.71 pF. How would I even begin to go about finding the total capacitance?
  43. P

    Positive Charge in Cube: Field Lines Distribution

    There is a positive charge 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? (can someone also give a clear definition of what uniformly distributed means?) describe how the field lines for the positive...
  44. D

    Understanding Body Diagonals of a Cube

    Can anyone out there tell me what the body diagonals of a cube are. I am asked to find the angle between the body diagonals of a cube. Seeing as how it is just the application of the dot product it does not seem difficult other than I do not know what body diagonals are (I have an idea but...
  45. D

    What are the body diagonals of a cube and how do you calculate them?

    Can some one tell me what are the diagonals of a cube? Picture is better
  46. E

    Electric flux through a cube problem

    Question: The cube in the figure (attachment) has sides of length L=10.0 {\rm cm}. The electric field is uniform, has a magnitude E=4.00 \times 10^{3} {\rm N}/{\rm C}, and is parallel to the xy-plane at an angle of 36.9^\circc measured from the + x - {\rm axis} toward the + y - {\rm axis}...
  47. S

    How to solve cube roots question ?

    How to solve cube roots question ? Example : x^3 - 100x^2 - 7800x + 16300 = 0 I had think long time but still cannot find the way. Besides trial an error, is there anyway to solve this problem ? thank you.
  48. G

    Can Cube Roots and Higher Roots Be Calculated Without a Calculator?

    there is a way of calculating the square root of any number (without using a calculator of course). is there a similar way, or any way, in fact to calculate cube roots, fourth roots, etc. again without using a calculator??
  49. quasar987

    Is the Mass of a Cube of Matter Determined by Its Total Energy?

    I wrote something on PF some time ago and nobody said what I wrote was wrong. But now I am almost certain that it is. What I said is that if you have a cube of matter, then its mass is E/c² where E is the total energy of its N constituents: E = \sum_i^N (m_ic^2 + K_i) I would correct that...
  50. G

    Electric Flux of Non-Uniform Field in a Cube: Solving for Flux and Total Charge

    The non uniformity of the electric field in the following question is throwing me off. If the electric field were uniform I'd have no problem. I assume I would use the following equation to solve for each of the surfaces: \Phi = \int \vec{E} \cdot d \vec{A} I'm having a difficult time...
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