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. I

    Geometry problem (angle of body diagonal of a cube)

    refer to the following image so consider the angle of the yellow theta on the top left. this is 45*. if we fix one side of both red lines at the blue circles, and we slide the other end along the green side of the cube, ie just think of the green lines as rails for the red lines to slide...
  2. M

    Understanding The Electric Flux of A Cube Rotated by an Angle Theta

    Hey, all, so I have been studying this problem all morning, and I do not understand two aspects to this example problem. I included a photo of the diagram used in this problem. You will see two cubes, but the diagram which corresponds to the problem below is the one on the right.PROBLEM: Find...
  3. R

    Angular Moment Cube: Calculating $\vec{L}$

    Homework Statement An homogeneous cube of mass M and side 2a spins around one diagonal of the faces with constant angular velocity w. Show that the size of the angular moment in relation to one of the fixed vertexes is \sqrt{\frac{43}{3}}Ma^2w What I visualize here is a cube with one of its...
  4. S

    MHB Infinite Sums Involving cube of Central Binomial Coefficient

    Show that $$ \begin{align*} \sum_{n=0}^\infty \binom{2n}{n}^3 \frac{(-1)^n}{4^{3n}} &= \frac{\Gamma\left(\frac{1}{8}\right)^2\Gamma\left(\frac{3}{8}\right)^2}{2^{7/2}\pi^3} \tag{1}\\ \sum_{n=0}^\infty \binom{2n}{n}^3 \frac{1}{4^{3n}}&= \frac{\pi}{\Gamma \left(\frac{3}{4}\right)^4}\tag{2}...
  5. ajayguhan

    Expression of bulk modulus of a cube in terms of strain

    In my text it's given when a cube underwents a uniform unit tensile force be applied in all six faces, bulk module=1/3(α-2β) Where α is longitudinal strain and β is lateral strain.is there a derviation for it..? And it states in x direction there will be increase in length and in y, z...
  6. K

    MHB Decomposition formulas for rotational symmetries of a cube

    I have a problem that I would like to check my work on. I am also stuck on the verifications for $E$ and $F$. Any help would be greatly appreciated. Thanks in advance. **Problem statement:** Let $G$ be the group of rotational symmetries of a cube, let $G_v, G_e, G_f$ be the stabilizers of a...
  7. K

    MHB Orders of elements for rotational symmetries of cube

    I am having lots of trouble doing this problem because I have particularly poor visualization skills. (Or maybe haven't developed them well yet). I would appreciate any help on this math problem. Here is the question: Suppose a cube is oriented before you so that from your point of view there...
  8. E

    Observing a cube approaching a black hole

    If a distant observer were to observe a large cube made of strong material approach a black hole, what would he see? ISTM that if one of the faces of the cube were to be the nearest approaching portion, he would see the four edges of the face become shorter and curved, and he would see the...
  9. V

    Area of a plane enclosed within a cube

    Homework Statement Find the area of the plane y=3x enclosed within the cube formed by the planes x=y=z= \pm 5 Homework Equations The Attempt at a Solution Using the equation y=3x, I found two points (x,y)=(5,1.66) and (x,y)=(-5,-1.66), then by plugging these points in the distance...
  10. twoski

    Newton's Method - Cube Root Of 5

    Homework Statement Use Newtons method to compute the cube root of 5. Do the first 10 iterations. x_{(0)}=1 determine the fixed points of the iteration and determine whether they are repelling/attracting. if attracting, then determine if the convergence is linear or quadratic. draw the...
  11. vmr101

    Calculate the electric flux piercing a cube?

    Homework Statement Consider four point charges q1, q2, q3 and q4, located at r1, r2, r3 and r4, respectively. (a) Calculate the electric flux piercing a cube (with side a and centered at r0 = (0, 0, 0) that contains all of these charges. (b) Calculate the electric field of the four charges...
  12. M

    Water pressure on base of cube

    "A cube of wood of side 4cm floats in fresh water with 1:4 showing above the surface. Calculate a) the water pressure on the base of the cube and b) the density of the wood" All I can work out is that the density of fresh water is 1000kgm^-3 and the area of the base is 1.6 x 10^-5 m...
  13. V

    Calculating Electric Fields on the Surface of a Charged Cube

    Homework Statement A cube of side a has a cube of side a/2 centered within it. The inner cube has a total charge Q that is uniformly distributed over its surface. A) For the surface of the outer cube, find: ∫s E * dA B) Is this sufficient information to find the electric fields at...
  14. T

    Electic Flux through a cube Why am I getting a value?

    Homework Statement A cubical Gaussian surface is placed in a uniform electric field as shown in the figure to the right. The length of each edge of the cube is 1.0 m. The uniform electric field has a magnitude of 5.0 * 10^8 N/C and passes through the left and right sides of the cube...
  15. K

    Calculating Electric Flux in a Nonuniform Field: A Cubic Box Example

    A cubic box of side a = 0.410 m is placed so that its edges are parallel to the coordinate axes, as shown in the figure. There is NO net electric charge inside the box, but the space in and around the box is filled with a nonuniform electric field of the following form: E(x,y,z) = Kz j + Ky k...
  16. D

    Find Flux Through Cube & Sphere

    Flux through sphere Homework Statement Given \vec{F}=\frac{\vec{r}}{r^2} and unit sphere, find the flux through the surface of the cube. Homework Equations Surface Integral of F dS=volume integral of Div. F d^3r The Attempt at a Solution After the above formula, I do not have...
  17. G

    How to find the moment of inertia of a cube?

    Hello, If I have a rigid cube rotated about an axis with dimensions L x W x H centimeters, how can we find the moment of inertia? Thank you.
  18. M

    Calculate flux through face of a cube

    Homework Statement A point charge q is located at the corner of a cube with edges of length L. Find the electric flux through the shaded face at y = L.Homework Equations Gauss's Law; flux = ∫E\bulletn dA = qenc/ε The Attempt at a Solution Here's what I'm thinking. In the problem statement...
  19. L

    Cube of Resistor Problem - Nice one

    Homework Statement Asymmetrical Cube - Determine the equivalent resistance between points A and C’ of the circuit below. Homework Equations U = R.i The Attempt at a Solution This problem was my professor that created. I know how to solve it, but I would like to know if other...
  20. J

    Surface Area of Cube & Inscribed Sphere

    Is there any relationship between the surface area of a cube and the surface area of the cube's inscribed sphere? Jean~
  21. M

    How do you rationalize a demoninator if the denominator is a cube root

    Hi, I know how to rationalize a denominator when it is a square root monomial or a square root binomial (through conjugation). For example, for a square-root monomial: 5/√25 = [5(√25)]/ [(√25)(√25)] = [5(√25)]/25 = (√25)/5 = 1 or -1and, for a square-root binomial: 5/(5 + √25) = 5(5 -...
  22. Y

    MHB How can I solve this integral involving cube roots?

    Hello I am working on this integral \[\int \frac{\sqrt[3]{x}}{(\sqrt[3]{x}+1)^{5}}\]I have tried using a substitution, I did: \[u=\sqrt[3]{x}+1\] and I got that the integral becomes: \[3\cdot \int \frac{(u-1)(u-1^{2})}{u^{5}}du\]I moved on from there, got a result, however it was not...
  23. A

    In Cube of resistances how to calculate current in one edge?

    Homework Statement Twelve resistors of equal resistance are connected so as to form a cube ABCDEFGH shown. Equivalent resistance between points A and G is 5/3 ohm. If a battery of voltage 100 V is connected across the points A and G, find the current (in ampere) flowing through the...
  24. C

    What direction is a shrinking cube going + logical problem

    To add to the oq - Is the "center" of an object an entirely logical construct? I draw a circle, find it's center and mark a point there. This point, no matter how small I mark/draw it takes up space (both physically and visually in my mind). Anything that takes up space has a center point...
  25. C

    Thermodynamics ice cube Problems

    Homework Statement I am working through a couple of revision sheets and have questions about the following two questions: 1) A)An ice cube of mass 0.03 kg at 0C is added to 0.2 kg of water at 20C in an insulated container. (a) Does all the ice melt? (b) What is the final temperature of the...
  26. L

    Heating up an Ice Cube - Is it Possible?

    I saw this video a long time ago and just assumed it was fake, but I just saw it again and honestly don't know how this is possible. Wouldn't the ice cube just instantly melt? https://www.youtube.com/watch?v=aLwaPP9cxT4
  27. T

    3 dimensional cube finding an angle

    Homework Statement A cube is positioned with its vertices at the following points: A=(0,0,0) C=(1,1,0) E=(0,0,1) G=(1,1,1) B=(1,0,0) D=(0,1,0) F=(1,0,1) H=(0,1,1) What is the angle of intersection of the planes formed by the triangles EBC and ECD Homework Equations AB=ABcosθ...
  28. A

    Engineering Torque of motor varies as the cube of the speed means what?

    is this means that torque is proportional or inversely proportional to the cube of speed the problem says The torque of a load driven by a 385-V, Dc shunt motor varies as the cube of the speed. The current taken by the motor is 51A at a certian speed. Calculate the additional resistance...
  29. J

    MHB Group Theory and a Rubik's Cube

    Does anyone know what this guy is on about? I understand some of the basics of group theory and I know there's a connection between Galois theory and the solving of a Rubik's cube, but I'm not sure what law he is even trying to disprove here. I'm assuming something with regards to symmetry or...
  30. T

    A cube balanced on edge falls.

    Homework Statement A homogeneous cube, each edge of which has a length \ell, is initially in a position of unstable equilibrium with one edge in contact with a horizontal plane. The cube is then given a small displacement and allowed to fall. Find the angular velocity of the cube when one face...
  31. B

    What is the Relationship Between Net Flux and Total Charge for a Cube?

    Homework Statement When is the net flux for a cube 0 and when is it not? Homework Equations ∫EdA= Q/8.85E-12 The Attempt at a Solution if you have no test charge then the flux of a cube is zero. but if you have a test charge then the net flux is the charge divided by 8.85E-12...
  32. Vorde

    Exploring the Possibility of Cube Matrices in Linear Algebra

    I just had my last Linear Algebra class, and I didn't get a chance to ask the one question that has been bugging me ever since we started in earnest with matrices. Why aren't there cube matrices? I mean, mathematical entities where numbers are 'laid out' in 3d not in 2d (not quite...
  33. S

    Deriving the Cube Root Formula with Newton-Rhapson's Method

    Homework Statement Derive cube root formula using Newton-Rhapson's method. x - y^3 = 0. Homework Equations xn + 1 = xn - f(xn)/f'(xn) The Attempt at a Solution I know that the solution is (2y + (x/y^2))/3 I tried using implicit differentiation and stuff but I can't get this out...
  34. B

    Intuition with applying Stoke's theorem to a cube.

    Homework Statement F(x,y,z) = xyzi+xyj+x^2yzk Surface is the top and four sides of cube with vertices at <+/-1,+/-1,+/-1> Homework Equations ∫∫curlF * ds = ∫F*dr The Attempt at a Solution At Z = 1, I broke up the surface into 4 lines, parameterized them and combined...
  35. N

    What Would Life Be Like on a Hypothetical Cube-Shaped Earth?

    Hypothetically, if the Earth were a cube, would walking to the corners(vertices etc.) feel like you were going uphill or would it feel flat?
  36. M

    Point charge at the center af a cube

    A 10 nC point charge is at the center of a 2.0m x 2.0m x 2.0 m cube. What is the electric flux through the top surface of the cube? related equations: gauss's law -- Qin/e0 e0 = 8.85 x 10 ^-12 C^2/Nm^2 my attempt: 10 x 10^-9 C ________________________ = 1129.94 C/Nm^2 8.85 x 10...
  37. C

    Triple integral problem - domain is that part of a cube btween 2 plane

    Homework Statement Evaluate the triple integral for the function \int\int\int y dV over that part of the cube 0 \leq x,y,z \leq 1 lying above the plane y +z = 1 and below the plane x+y+z = 2 Homework Equations The Attempt at a Solution This is the first attempt at a triple...
  38. G

    Strings holding a cube from above and below

    I was watching a Walter Lewin lecture on Newton's laws (which was great, by the way), and at the end, he presented this problem; There's a string hanging from the ceiling (actually not the ceiling, it was just a surface), and a cube is hanging from that string. There is another string, attached...
  39. M

    What is the area of intersection between two adjacent spherical caps?

    Ok, so a cube and a sphere are both centered at origo. The cube has side lengths L. I need to know the surface area of the part of the sphere that is inside the cube, for all possible r. There will be three different equations, one for 0 < r < L/2, when the entire sphere is inside the cube, one...
  40. R

    Calculating the buoyant force on a cube

    Homework Statement A cube, with a volume of 0.78 m3 is submerged in a swimming pool. What is the buoyant force acting on the object if it has a mass of 328 kg? Homework Equations The Attempt at a Solution
  41. H

    Electric Flux Through a Face of a Cube

    Homework Statement A point charge +Q is placed at the center of a cube. What is the electric flux through a face of the cube? Homework Equations Flux = Q/ε The Attempt at a Solution The answer is Q/(4ε), but I thought it should be Q/(6ε) which isn't even an option. I'm I crazy? Since there...
  42. A

    MHB Find the finite sum of the square and cube exponent of integers

    Hey, it is clear for me that \sum_{i=1}^{n} i = \frac{n(n+1)}{2} how to find a formula for \sum_{i=1}^{n} i^2 \sum_{i=1}^{n} i^3 Thanks
  43. J

    Electric potential inside a cube

    Homework Statement A metal box has 6 walls, all insulated from one another. The left and right wall are held at V= V0, which are at y=-d and y=d. All the other walls are grounded. The cube has dimensions where walls run from x=0 to x=2d, z=0 to z=2d, and y=-d to y=d. Homework...
  44. M

    Calculute the flux resulting from a certain vector field in a cube.

    Let's say there is a cube sitting in the first octant. Our F(x,y,z): <ax , by, cz> and Each face of the cube is oriented to outward pointing normal. Can I just calculate the the flux of one face and then multiply this by the number of faces to get the total flux? Will flux in a cube always be...
  45. C

    Does EM Radiation Dissipate at a 1/r^5 Ratio for Circularly Polarized Waves?

    inverse square vs cube = ? If the electric field falls off at the inverse square ratio, and magnetic at inverse cube, does EM radiation dissipate at 1/r^5 ratio for circularly polarized waves?
  46. B

    Electric Flux and Charge Distribution in a Cube with Uniform Electric Fields

    Homework Statement Hello, the problem I am working on is: Assume the magnitude of the electric field on each face of the cube of edge L = 1.05 m in the figure below is uniform and the directions of the fields on each face are as indicated. (Take E1 = 31.5 N/C and E2 = 26.5 N/C.) (a) Find...
  47. J

    Calculate the flux through a cube of size 1.0 m

    An E field exists in a region of space and it can be described by: \bar{E} = \hat{i}xy^2 Calculate the flux through a cube of size 1.0m, with one end extending into the positive x,y and z directions. Find the charge enclosed. I have no idea how to start this? can someone point me in...
  48. anemone

    MHB Rationalizing a denominator involving the sum of 3 cube roots

    Hi members of the forum, Problem: Rationalize the denominator of $\displaystyle \frac{1}{a^\frac{1}{3}+b^{\frac{1}{3}}+c^{\frac{1}{3}}}.$ I know that if we are asked to rationalize, say, something like $\displaystyle \frac{1}{1+2^{\frac{1}{3}}}$, what we could do is the following...
  49. R

    Electric Flux thru the top face of a cube

    Homework Statement An electric field given by \vec E = 4.0 \hat i - 3.0(y^2+2) \hat j pierces a 2.0 meter by 2.0 meter by 2.0 meter cube. What is the electric flux thru the top face? Homework Equations \phi = \int \vec E \cdot d \vec A The Attempt at a Solution I'm aware that you...
  50. A

    Using a cube as a Gaussian surface

    Homework Statement Suppose there is a uniformly charged cube with known side length. I then imagine a larger, closed cube surface surrounding it. This larger cube has double the side length and is symmetrical to the smaller cube. Is is practical to use this Gaussian surface to compute the...
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