Cubes: Elements, Properties, Volume and Surface Area Formulas and Examples of Problems
Cube: Elements, Properties, Volume and Surface Area Formulas and Examples of Problems – How to calculate the volume and surface area of a cube?, On this occasion About the knowledge.co.id will discuss it and of course about other things that also cover it. Let's look at the discussion together in the article below to better understand it.
Cubes: Elements, Properties, Volume and Surface Area Formulas and Examples of Problems
A cube shape is a spatial figure that has a three-dimensional shape which is bounded by six sides and the sides are congruent or square.
Then the Cube Space Build can also be called a regular hexagon which is similar in shape to a rectangular prism.
Cube Elements
We can see together with the cube image above, pay close attention because we get an element - the elements of the cube above, namely below:
- Side or field
Understanding the side of the cube is the field that limits the cube. If we look at the cube image above, we can conclude that a cube is a geometric shape that has 6 sides, all of which are square.
And the sides are:
- Down side ( ABCD )
- The upside ( EFGH )
- Front side ( ABFE )
- Back side ( DCGH )
- Left side (BCGF)
- Right lateral side ( ADHE )
-
Lateral
The edge of the cube means the secant line between the 2 sides of the cube and looks like the framework that makes up the cube.
Then the ribs from the cube image above are AB, BC, CD, DA, AE, BF, CG, DH, EF, FG, GH, and HE.
- Corner point
Corners are points of intersection between 2 or 3 edges. In the cube image above, we can get the angles, which have 8 angles, namely A, B, C, D, E, F, G, and H.
- Plane diagonal or side diagonal
If we give a long line at each of its opposite angles on each side then we will see the shape of an isosceles triangle, now that line is what is referred to as a diagonal field or side.
In the example of the cube image above, we can find 12 diagonal planes or 12 sides, namely AF, BE, BG, FC, CH, DG, AH, DE, BD, AC, EG, and HG.
- Space diagonals
The space diagonal is a line that connects 2 opposite corner points in one space.
In the cube example above, we can get 4 space diagonals, namely the lines BH, DF, AG, and EC.
- Diagonal field
The definition of a diagonal field itself is a field formed from 2 diagonal lines of the field and 2 parallel cube edges.
In the cube example above, we can get 4 diagonal fields, namely ACGE, DBFH, ABGH, EFCG.
Properties of the Cube
Next we discuss the properties of a cube, which consists of:
In the image of the cube above, we can see that the cube consists of: ABCD.EFGH in each corner which has the following properties:
- All Sides of a Square Cube:
If you pay attention, on the sides ABCD, EFGH, ABFE, DCGH, BCGF and so on have a square shape and have the same area.
- All Sides of a Cube are the Same Length:
The cube edges, namely: AB, BC, CD, DA, EF, FG, GH, HE and so on, have the same length.
- Each side diagonal of a cube has the same length:
Look at the line segments BG and CF in the ABCD.EFGH cube image. The two lines are a diagonal of the ABCD.EFGH cube in the BCGF plane which has the same length.
- Each space diagonal in a cube shape has the same length:
From the ABCD.EFGH cube image above, there are 4 space diagonals, namely HB, DF, AG and CE, all of which are the same length.
5. Each Diagonal Field in a Cube Shape Has a Rectangle Shape:
Look at the ACGE diagonal in the ABCD.EFGH cube image above. It is clear that the diagonal area has a rectangular shape.
Cube Volume Formula
Now, after explaining the meaning of a cube and what elements are in a cubic shape. Now we will explain the formula for the area and volume of the cube itself, which is as follows:
V = S3
Information :
- V = volume of the cube ( cm3 )
- S = side length of the cube (cm)
As for the formula for the area of the cube itself is as follows:
The formula for the area of a cube
L = 6.s2
Information :
- L = surface area of the cube ( cm )
- S = side length of the cube (cm)
Cube Surface Formula
-
Surface Area of the Cube :
- L = 6 x rib x rib = 6 x s2
-
Circumference of the Surface of the Cube :
- K = 12 x rib = 12 x s
Example of a Cube Problem
Problem 1:
It is known that a cubic shape with a side length of a cube is 30 cm, then calculate the volume, circumference and surface area of the cube!
Answer and discussion:
The formula for Volume of a Cube = V = s³
So Vol = 30 x 30 x 30
Volume = 27000 m³
Circumference Formula for a Cube = K = 12 x s
K = 12 x 30
= 360 cm
The formula for the surface area of a cube = L = 6 x s²
L = 6 x 30 x 30
L 5400 cm²
Problem 2:
Budi's wardrobe is in the shape of a cube which has the same length, width and sides, which are 4 meters. What is the volume of Budi's wardrobe?
Answers and discussion:
If it has been stated that it has the same length, width, and sides, it is no longer wrong to say it is one of the properties of a cube, therefore it can be directly calculated the volume of the cupboard as following:
Wardrobe volume: 4³ = 4 x 4 x 4 = 64 m³
Problem 3
There is a surface of a cube whose side length is = 10 cm. Find and calculate the surface area of the cube!
Resolution:
Given: s = 10 cm
asked: L = …?
Answer :
L = 6 x s2
L = 6 x 10 x 10
L = 600 cm2
So, the surface area of the cube is = 600 cm2
Problem 4
It is known that the volume of a cube is 1331 cm3 but the length of the edge of the cube doesn't exist yet, so you have to find out how long the edge of the cube is?
Answer :
It is known = v = 1331 cm3
When asked = the length of the edge of the cube?
Volume = s.s3
1331 cm3 = s3
1331 = 11
S = 11 cm
So, the side length of the cube is 11 cm.
Thus the review from About the knowledge.co.id about Cubes: Elements, Properties, Volume and Surface Area Formulas and Examples of Problems, hopefully can add to your insight and knowledge. Thank you for visiting and don't forget to read other articles.
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