√ Definition of a Cube (Definition, Net, Area and Volume, Example Problems)
Definition of Cube
Look at the following drawing of the room.
This space is a cubic space. A cube is a geometric figure bounded by six square sides.
From the picture above, can you mention the characteristics of a cube?
A cube has six sides that are the same size (congruent), has eight vertices, and twelve edges that are the same length.
We can name the above cube as ABCD.EFGH cube. Next we will learn about some examples of implementing cubes.
Cubes in Everyday Life
We encounter many objects that resemble cubes. Have you ever played monopoly or snakes and ladders?
In this game we use dice that have a cube-like shape.
Dice have six sides, each side of which has a die of 1 – 6. Next we will discuss the edges, space diagonals, diagonal planes, and cube nets.
Cube Ribs
Look again at the cube in Figure 1 above.
How many edges are in the cube ABCD.EFGH?
- There are 12 edges in the cube.
- The edges of a cube are the same length.
- AB ribs parallel to ribs CD, EF, and GH.
- The ribs BC are parallel to the ribs AD, EH and FG.
- The AE ribs are parallel to the BF, CG, and DH ribs.
Diagonals of the Space Cube
Look at the following picture.
A cube has four space diagonals that connect two opposite corners.
There are such spaces, including AG, BH, CE, and DF.
Suppose the length of the edge of the cube is r, then the length of the diagonal of the cubical space ie
AC = √(AB2 + BC2) = √(r2 + r2) = √(2r2) = r √2
AG = √(AC2 +CG2) = √((r √2)2 + r2) = √(3r2) = r √3
So, the length of the space diagonal of the cube with the edges r is r √3.
The Diagonals of the Cube
Consider one of the diagonals of the cube below.
The image is one of the diagonal planes of the cube, namely the diagonal plane ABGH.
Can you name the other diagonals?
The other cube diagonal planes are the CDEF, ADGF, BCHE, ACGE, and BFHD diagonal planes. So there are 6 diagonal fields in the cube.
The diagonals of a cube have the same area. Suppose the length of the edge of the cube is r, then the area of the diagonal area (eg the diagonal area of ABGH):
The formula for the area of a diagonal cube
BG = √(BC2 +CG2) = √(r2 + r2) = √(2r2) = r √2
Diagonal area = AB x BG
Diagonal area = r x r √2 = r2 √2
Information:
r: the length of the edge of the cube
Cube Nets
There are many grids of cubes that can be created. In this article, we will present two examples of cube nets.
Consider the nets of the following cubes.
In the two nets of the cube, the parts of the same color are the sides of the cube that face each other.
The net of cubes is composed of six equal (congruent) squares.
In the second cube net there are codes from I to VI.
Square I is opposite square IV, square II is opposite square V, and square III is opposite square VI.
Next, we will explain some formulas on the cube.
Cube Formula
The formulas that will be presented in this section include the formula for the surface area of a cube and the volume of a cube.
Surface Area of a Cube
Look at the following picture.
Previously we have discussed about cube nets. Using the net of cubes we can determine the formula for the surface area of a cube.
The cube is composed of six square sides. Suppose the length of the edge of the cube is r, then the surface area is:
The formula for the surface area of a cube
Area I = Area II = Area III = Area IV = Area V = Area VI = Area of the square
Area of the square = r x r
Surface area of a cube = Area I + Area II + Area III + Area IV + Area V + Area VI
Lp = (r x r) + (r x r) + (r x r) + (r x r) + (r x r) +(r x r)
Lp = 6 x r x r = 6r2
Information:
- Lp: surface area of the cube
- r: the length of the edge of the cube
Next is explained about the volume of the cube.
Cube Volumes
Look at the following picture
In the picture above there is a cube ABCD.EFGH with side lengths r.
In general, the volume of a prism is the area of the base multiplied by the height of the prism.
Because the base of a cube is a square with side lengths r, then the area of the base is r2.
Cube Volume Formula
Volume of cube = area of base x height
Volume of cube = Area of square x height
V = r2 x r
V = r3
Information:
- V: volume of the cube
- r : the length of the edge of the cube
Do the following practice questions.
Questions and Discussion
Consider a cube with a side length of 8 cm. Define:
- The diagonal size of the cube space,
- The area of the diagonal of the cube,
- The surface area of the cube, and
- Cube volume
Discussion
- Diagonal size of space
Space diagonals = r √3 = 8√3 cm
- Diagonal area
Diagonal area = r2 √2 = 82 √2 = 64 √2 cm2
- Surface area of the cube
Lp = 6 x r2 = 6 x 82 = 6 x 64 cm2 = 384 cm2
- Cube volume
V = r3 = 83 = 512 cm3
Let's summarize the cube material in this article.
Conclusion
- A cube is a geometric figure bounded by six square sides.
- A cube has 12 edges that are the same length.
- A cube has four congruent space diagonals.
- A cube has six congruent diagonals.
- Cubes have various grids.
If there is a cube with edges r, so:
- The diagonal of the space is r √3
- The area of the diagonal is r2 √2
- The surface area of the cube is 6 x r2
- The volume of the cube is r3.
That's all the information that can be conveyed. Hope it is useful.
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