how we can derive the formula of the surface area of a cube?

Question

maybe its more on proving where the formula get

Answer 1

I am pretty sure that this is an axiom for Euclidean geometry.

For area, there are two axioms that are used:
1. The area of a square with sides of length 1 is 1.
2. The area of a square with sides of length a is a^2.

The axiom used will depend on the text and the preference of the instructor.

So, the surface area of a cube will either be 6*1=6 or 6*a^2 square units.

For the volume formula, the fact that the volume of a cube with sides of length 1 is 1 cubic unit, defines the volume of the cube. And, from that axiom, the volumes of all Euclidean solids will be able to be derived.

Note: As with finding the area of a circle, finding the volume of a sphere will involve a limiting procedure and hence calculus; the volume of a sphere will not be a consequence of the axioms of Euclidean geometry.

Answer 2

Thank heavens for beer, mobile phones and in this case Jim R! who correctly states that a cube, by definition is only made up of squares.

Since the area of a square is a^2 ('a' being the length of one side of the square) and there are six faces on a cube, the surface area of a cube will be 6a^2 as someone already stated.

Answer 3

How many people missed third grade math and don't understand that a cube has square sides. If the sides are rectangular, it is NOT a cube.

Surface area of a cube is 6 * a^2

Answer 4

Surface Area of a Cube formula

cube = 6a²

Answer 5

All the above answers are incomplete.

A cube is a three-dimensional shape with six square or rectangular sides. The above answers deal only with the case of square sides. What about rectangular sides? Well, in this case you have two different faces of which 4 eqaul areas differ from the other 2 equal areas. So you calculate total surface area as follows:

4*(length1*width)+2*(length2*width)
or
width*(4*length1+2*length2)

Answer 6

Now that you know this, try deriving the formula for the length of a diagonal of a cube.

Answer 7

asuming the cude is a regular cube (all sides are squares) it will be
6 * (length)^2
the six is for 6 faces of the cube
and since each face is a square it has a area of length * breadth which are equal in a square hence length * length = lenght^2

if the cube is not a regular cude(sides are rectangles) it will be
2*((breadth*height) + (height * width) +(width*breadth))
we have a 2 as in a cude there are 2 opposite panels that have the same area

Answer 8

it is derived by first doing the product of all the basic dimension ie lenth times bredth and so on...this is then multipleid by no of such similar faces on the cube

Answer 9

let each side of cube = "a"
area of each face= (side)^2
(since each face is a square)
total no of faces = 6
total area= 6(area of one face)
6a^2

Answer 10

exactly wat the above guy said. since he already had the formular u have it its only fair i get the10 points. oh n if u generous i'd appreciate a thumbs up from both of u