Tất tần tật kiến thức về khối lập phương trong hình học

The cube is one of the geometric knowledge that students are familiar with from grade 1. To help you better understand this type of geometry, as well as grasp the most basic knowledge about shapes, let’s explore more details with Nguyễn Tất Thành in the following article.

What is a cube?

In all types of geometry, the cube is known as a 3-dimensional platonic solid, made up of 12 equal sides. In particular, all 6 faces of the block are squares with 8 vertices corresponding to 8 points.

Bạn đang xem: Tất tần tật kiến thức về khối lập phương trong hình học

Characteristic properties of cubes

A block is considered a cube when it has the following properties:

• A cube with 6 planes is an equal symmetrical square

• A cube has 12 equal sides

• The diagonals of the sides are equal

• The diagonals of a cube are equal

Cube identification sign

To be able to recognize a cube, we can rely on the following characteristics:

• The sides of the figure are 6 equal squares

• The diagonal sides are of equal length.

• The cube has diagonals that are also of equal length.

Formulas related to cubes

When learning about basic cube knowledge, students need to clearly understand the formulas related to the shape. Specifically:

General: For a cube with side a, the side diagonal is d, and the diagonal of the cube is D

Circumference formula

P= 12.a

In there:

Formula for calculating area

The area of ​​a cube will be divided into two types: total area and surrounding area. Specifically:

The area of ​​a cube is divided into two types: surrounding area and total area

* The formula for calculating the surrounding area of ​​a cube is:

Sxq = a2.4

In there:

*Formula to calculate the total area of ​​a cube

Stp = a2.6

In there:

Formula for calculating volume

To calculate the volume of a cube, apply the formula:

V =aaa= a3

In there:

Formula to calculate the diagonal of a cube

In a cube, the diagonal of the shape will join the heights to form a right triangle

Applying the Pythagorean theorem, we have the formula to calculate diagonal D:

In there:

• D is the length of the diagonal of the cube

• d is the length of one side’s diagonal

• a is the side length of the cube

Instructions on how to draw a cube in mathematics

To draw the cube ABCDEFGH

• Step 1: Draw the base of cube ABCDEFGH as square ABCD

• Step 2: Take turns constructing altitudes of length a corresponding to the vertices of the bottom surface, we get the corresponding altitudes AE,BF,CG,DH=a.

• Step 3: Connect the vertices E, F, G, H together to get the cube ABCDEFGH

* Note: Draw dashed lines for AD, DC, FD because these are filled segments.

Common types of exercises about cubes at elementary school level

As for knowledge about the cube, most of it will be learned from grade 1. However, this is the stage where children will be new to shapes and knowledge, so the exercises are also basic as follows. :

Form 1: Formula – definition

This is the type of multiple-choice exercise that appears in math exams that children will often encounter. With this type of math, you will often rely on theoretical knowledge of definitions and formulas to ask questions.

Therefore, to solve this exercise requires students to firmly grasp the theory and basic knowledge of cubes to give the most accurate answer.

For example: Which statement is correct about the cube?

A. A cube with 6 planes is an equal symmetrical square

B. The cube has unequal diagonals

C. A cube has 10 equal sides

D. Both A, B, and C are wrong

==> By definition, the property of a cube will be that it has 6 planes that are equal symmetrical squares, with 12 equal sides and equal diagonals. So the most accurate answer is A.

Type 2: Observe pictures, identify rectangular and cube objects

This is one of the most basic exercises to increase your baby’s ability to recognize and observe better. Usually the test will give you a series of different images and identify which one is a cube.

With this type of exercise, many students are often confused with rectangular shapes, so they are required to clearly recognize the properties of cubes to choose the correct answer.

For example: Which of the following objects is a cube?

Solution:

Based on the characteristics of a cube, it will have 6 equal square faces, so in the picture there will be a gift box and a cube of dice.

Form 3: Counting cubes

When doing exercises about cubes, children will get acquainted with the corresponding form of counting exercises. This means your baby will look at the picture and count how many shapes there are.

For example:

Form 4: Name objects that are cube-shaped

This is a fairly common type of exercise in elementary school math programs, to determine whether your child really understands the cube or not. Therefore, this form of math will force children to think and think about the shape of a cube in reality to come up with the correct answer.

Example: Name 5 objects that are cube-shaped

Prize: Gift box, rubik’s cube, square stool, square fish tank, mini speaker.

Form 5: Calculate the area/perimeter/volume of a cube

This will be a more advanced form of cube exercises, where the problem will require students to accurately calculate the area, perimeter or volume of the shape. Therefore, you will have to clearly understand the above formulas to solve the exercises correctly.

For example: A cube A has an area of ​​384 cm². What is the volume of that cube?

Solution:

The area of ​​one face of a cube is: 384 : 6 = 64 cm²

The side length of the cube is 8cm because 64 = 8 x 8.

So, the volume of the cube is 8 x 8 x 8 = 5126 cm³

The secret to helping children learn cube math effectively

Because elementary school children will often only be familiar with basic knowledge about the cube, but that is the foundation for learning more advanced knowledge. Therefore, below are some tips to help improve children’s learning efficiency that parents can apply:

Build a solid math foundation for your child with Nguyễn Tất Thành Math

Nguyễn Tất Thành Math is a mental English math learning application for preschool and elementary school children that is being chosen by many parents. Because this is the age where thinking begins to develop and form, equipping your child with knowledge at this stage will effectively create a solid mathematical foundation for him.

In particular, with active teaching methods, children are interested in learning, understand the roots of math problems and think independently to solve problems. So while learning with Nguyễn Tất Thành Math, your child will:

In addition, Nguyễn Tất Thành Math also provides children with:

• 60+ math topics based on 7 main math topics, including geometry.

• With 4 levels from easy to difficult (Including 400+ in-depth lessons)

• And more than 10,000+ interactive activities increase the excitement and joy of learning

When participating in the course, children will be guided to learn from basic to advanced knowledge in a methodical and in-depth manner. In particular, combining with interactive activities such as playing games, solving puzzles, etc. will avoid causing boredom for children.

We guarantee that Nguyễn Tất Thành Math will help your child have fun, exciting and much more effective math lessons.

Download Nguyễn Tất Thành Math for Android phones

Download Nguyễn Tất Thành Math for iOS phones

Make sure your child has a solid understanding of the cube

Xem thêm : Soạn bài Chuyện bốn mùa lớp 2 tập 2 sách Kết nối tri thức chi tiết nhất

To conquer exercises about cubes, children are required to master the theory of this knowledge from formulas, definitions, characteristics, properties, types of exercises…

Because only when your child masters it will he be sure he understands the exercises and solves them correctly.

Therefore, parents should regularly ask questions, check their children’s books, etc. to see if their children remember or understand this picture. From there, reinforce weak knowledge in a timely manner, avoiding being overloaded with theories that will make it difficult for your child to absorb.

More practice is indispensable

Besides learning and mastering the theory, parents should create conditions for their children to practice and practice more through: Doing lots of exercises, applying learning in practice, organizing related games. Go to the cube for your baby to participate,…

Regular practice will help children understand and remember knowledge better. At the same time, this is also an effective method to help children increase their interest in learning.

Some notes when teaching children to learn cubes

To improve effectiveness when teaching children about cubes, parents need to pay attention to the following issues:

• Parents need to clearly explain to their children the characteristics and properties of this shape.

• Children often confuse cubes with rectangles, so parents should show children the difference to recognize them.

• Parents should let their children learn through games to help them absorb knowledge more naturally and effectively.

• Use practical examples with objects and objects that resemble cubes so that children can easily visualize and absorb the lesson.

H2: Some exercises about cubes for children to practice on their own

After you have firmly grasped the theory, here are some exercises for your child to practice with:

Question 1:

Cube A has sides of 4 cm. Cube B has sides twice as long as the sides of cube A.

Ask how many times the volume of cube B is the volume of cube A.

Question 2: A cube-shaped metal block has a side of 1/5 m. Each cubic centimeter of needle weighs 6.2 g. How many kilograms does that block of metal weigh?

Question 3: A cube has a total area of ​​294 cm². What is the volume of that cube?

Question 4: A cube has sides of 7 cm. If the edge of a cube increases by 4 times. Ask:

a) How many times does the total area of ​​the cube increase?

b) How many times does the volume of a cube increase?

Question 5: How many small cubes with sides of 1cm must be arranged to get a large cube with a total area of ​​294dm²

Question 6: A rectangular glass tank has a bottom area of ​​250cm² and the tank is containing water. Calculate the height of the water level, knowing that if you put a metal cube with a side of 10cm in the tank, the cube will just be submerged in water (the bottom on the cube is equal to the water surface).

Question 7. People make a cube-shaped iron cage with each side length of 25dm. Each square meter of iron costs 45,000 VND. How much did it cost to make that iron cage?

Question 8. Uncle Binh needs to make 2 cube-shaped iron barrels without lids with sides of 1.8 m. Ask Uncle to paint both the inside and outside of those 2 barrels, how many kilograms of paint must be purchased, knowing that for every 20 m2, 5 kg of paint is needed.

Question 9:

Question 10:

Question 11: Write in the dots

• The Rubik’s Cube has the shape of a cube………………

• The ball has the shape of a block ……………………..

• The pen box has a block shape ……………………..

• The glue box comes in block form………………

Question 12: Which of the following shapes is a cube?

Question 13: Is each of the following objects shaped like a cube or a rectangular box?

Question 14: Name real objects:

a, Has the shape of a rectangular block.

b, Cube shaped.

Conclude

Above is information about basic cube knowledge. This is a quite difficult shape, so parents need to accompany them to help their children understand, remember and practice effectively. Hopefully the knowledge and tips that Nguyễn Tất Thành shares will help best teach children to learn these shapes.

Nguồn: https://truongnguyentatthanh.edu.vn
Danh mục: Giáo dục