What is surface area of a cube ?
To find the definition of the surface area of a cube we first need to give the definition to its components – the cube and the surface area.
Due to geometry, cube should have such facilities:
- It is built in three dimensions
- It is solid object
- Cube is bounded by six square faces (sides, facets)
- Cube has three meetings at each vertex
- It has 12 edges and 8 vertices
There is such thing as Platonic solids and cube is one of them. There are five Platonic solids – Tetrahedron (with four faces), Cube (or hexahedron with six faces), Octahedron (eight faces), Dodecahedron (twelve faces) and Icosahedron (with twenty faces). Cube is the only regular hexahedron (and the surface area of a cube is the simplest from all of the Platonic solids).
Cube is the original figure and combines a lot of facilities in itself. Did you know that cube is an equilateral cuboid, a square parallelepiped, a right rhombohedron, a trigonal trapezohedron in four orientations and a regular square prism in three orientations at the same time? The cube has cubical or octahedral symmetry; is dual to the octahedron. Have you ever heard about something so interesting and unusual? At the same time cubes are integral part of our lives nowadays. That is why we see cubes and the surface area of a cube like something usual.
If we will look at orthogonal projections of cub, we will see that there are four of them (The first and third correspond to the A2 and B2 Coxeter planes):
- Centered on a vertex
- Centered on edges
- Centered on a face
- Normal to its vertex figure
After we gave the definition to the cube, we need to find what is the surface area, before trying to find the surface area of a cube. Every solid object has a surface area – it is a measure of the total area that the surface of an object occupies. The general definition of the surface area is not so old comparing to other definitions in math and geometry. It was found by Henri Lebesgue and Hermann Minkowski in the end of the nineteenth century – beginning of the twentieth century. Their geometric measure theory studies various notions of surface area for irregular objects of any dimension. Actually, the definition of the surface area of a cube was given a lot earlier.
Simple definition of the surface area of the solid object is the combined area of all of the sides on its surface. That is why the surface area of a cube is the combined area of its six sides.
How to find the surface area of a cube ?
Cube’s six sides are equal, so if you need to find the surface area of a cube, you just need to find the surface area of one side and then multiply it by six. There are two easy ways to find the surface area of a cube :
- When you know the length of one cube’s side
- When you know the volume
- If you know the length of one side, you can find the surface area of a cube in two easy steps:
- First you need to find the surface area of one side of the cube. Every side of the cube is a square. The surface are of the square is side length multiplied by it. Or if the one side length is “s” than square surface area will bes2. For example, if the length of the side is 6 cm, then the surface area of the square will be 6*6=36 cm2. Don’t forget to state your answer in square units.
- When you know the surface area of the square (one of the cube’s faces), you can simply find the surface area of a cube. Remember, that all six faces of the cube are equal. So, to find surface area of a cube you just need to multiply the surface square of one side by six. For example, if the surface area of one face is 36 cm2, then the surface area of a cube will be 36 cm2 multiplied by six – 36 cm2*6=216 cm2. Again, don’t forget to state your answer in square units
If you know the volume of the cube, you can find the surface area of a cube easy three steps:
- First you need to take the square root of the cubes’ volume with the help of some counting device. It is easy – just push one button on the calculator. For example, our cube has volume 125 cm3. This is actually a perfect cube, because the square root of its volume will give us a whole number. It is useful for the example. But you need to know that the cube’s volume will not always give the whole numbers. In our case, if we have such perfect cube’s volume, we will find that the cube root is 5 (5 x 5 x 5 = 125). Then, we can say that the length of the one side is 5 cm. Now we can do the procedure from the first way to find the surface area of a cube
- Find the surface area of the cube’s one face (side). In our example this will be 5 x 5 = 25 cm2 (again, square units)
- Now you can finally find the surface area of a cube. In our example this will be 25 x 6 = 150 cm2
If you need to find the surface area of a cube quickly, you can use an automatic program. There are plenty of online platforms on the different websites and also in applications for different gadgets and platforms (Android, Apple, and etcetera). This simple programs work with the surface area of a cube the same way as you will. So all you need to do is to fill one of the fields – the length of the one side or the volume of the cube.
The surface area of a cube is very important for many businesses. For example, companies package items in boxes use it very often. It is important to find how much cardboard will they need to make every box. Companies need to know all this to determine the costs and the amount they need to make the boxes. As you can see, the surface area of a cube is not difficult to find. Especially, if we will compare it to surface areas of some other bigger Platonic solids – Octahedron (eight faces), Dodecahedron (twelve faces) and Icosahedron (with twenty faces).
Anyway, some companies have to work with the surface area of a cube day by day and give very quick and correct results. That is why they use automatic programs to find thesurface area of a cube.
Interesting facts about the cube
As you already know, the cube is so interesting and at the same time so usual figure. Now, when you know how to find the surface area of a cube, let’s see some other interesting aspects, geometric relations and facts about the cube.
If you are going to make a detail to make a cube from paper, you can do it in eleven different ways:
- It can be a simple detail with three horizontal squares on top and three vertical squares under the middle horizontal square – they form a letter T
- The other funny cube detail is almost like the first T detail, but it has one square above the middle square in horizontal line and only two under it
- This detail is similar to the detain number one, but the left horizontal square is shifted down on one square
- Same as the previous detail, this detail is similar to the detain number one, but the left horizontal square is shifted down on two squares
- Again, same as the previous detail, the left horizontal square is shifted down on three squares
- This detail is similar to the detain number two, but the top square is shifted from the middle to the right side
- This detail is similar to the detain number six, but the left horizontal square is shifted down on one square
- This detail is also simple – two vertical lines are made from three squares each. This lines connects one with the top and one with the bottom and form one horizontal line from two squares
- This detail is like a snake from the old computer game. Three vertical lines made from two squares each other. They connected with each other and form a ladder
- This detail is similar to the detail number 5, but the middle square from the vertical line is shifted down under the left horizontal line
- This detail is similar to the detain number two, but the left horizontal square is shifted down on one square
All this details can show you graphically, how to find the surface area of a cube. You can see, that in every way constructing we still have six squares and this six squares form the cube. In this way, you can see that the surface area of a cube is the total surface area of six square.
Cube and the surface area of a cube are quite popular in art, science and games. It is a magic figure. You probably have heard of these things:
- Diamond cubic (crystal structure is a repeating pattern of 8 atoms that certain materials may adopt as they solidify)
- Necker cube (It is an optical illusion)
- OLAP cube (online analytical processing, the term cube here refers to a multi-dimensional dataset. Sometimes it is called a hypercube if the number of dimensions is greater than three)
- Unit cube (a cube with sides with 1 unit length. The idea is that the volume of a 3-dimensional unit cube is 1 cubic unit. Now you can understand that the total surface area is 6 square units)
- Prince Rupert’s cube (it was found after the unit cube. It is the largest cube that can go right through a hole cut in a unit cube, that means through a cube with sides with length1, without splitting the cube into two pieces)
- Rubik’s cube
- Yoshimoto cube
The Necker cube was first published as a rhomboid in 1832 by Swiss crystallographer Louis Albert Necker. This illusion makes people see that one side of the cube goes under another and looks fantastic. This cube gave a lot of ideas to other arts. Yoshimoto cube is not so popular these days as Rubik’s cube, but it is very exciting and developmental. It is a polyhedral mechanical puzzle toy. Yoshimoto cube was invented in 1971 by Naoki Yoshimoto. Naoki discovered that two stellated rhombic dodecahedra could be pieced together into a cube when he was finding different ways he could split a cube equally in half. Rubik’s cube is the most popular cube-game in the world. More than 350 million cubes had been sold worldwide. Nowadays it has a lot of modifications – 2×2, 4×4, 11×11 and a lot of others. Anyway, the most popular Rubik’s cube is 3×3. A lot of challenges with Rubik’s cube keep people together. This game was used even in modern IT technologies. For example, Google used twenty professional Rubik’s cube gamers to make algorithms.
Rubik’s cube is hard to solve. The best result for human is 5.55 sec nowadays. This record was reached by Mats Valk who lives in Netherlands. However, Smartphone-powered Lego robots can solve it faster than humans – in 5.352 sec. Anyway, humans are still the best in doing something beautiful, unusual and challenging. For example, Marcell Endrey solved cube blindfolded in 28.80 seconds. Chinese two-year old child did it in less than two minutes. Rubik’s Cube is unusual game and the most popular in the world for all times. More than 350 million Rubik’s Cubes have been sold worldwide.
A Rubik’s Cube has over 43 quintillion different possible configurations. It will take you a lot of time to try each one, even if you’ll do one in each second. Actually, the number will be huge – more than 1400 trillion years (it is longer than from the Big Bang to nowadays). The world’s largest Rubik’s Cube is located in Knoxville, Tennessee, while the smallest was made by Russian Evgeniy Grigoriev. They are three meters and 10mm wide, respectively. Actually, first cube is also the heaviest – it weights over 500 kilograms.
Now you know a lot about the cube. You know how to find the surface area of a cube, how it used and how to make it from paper. If you need some other interesting information, you can find it here. Our professional writers will be also happy to help you with cover letter, research proposal, writing a persuasive essay, writing assignments show you how to write a coursework. Remember, that you can do everything, you just need to try.
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