Cách tính thể tính hình hộp chữ nhật chính xác và dễ nhớ

The volume of a rectangular box is one of the basic forms of math, popular in both learning and practice. Therefore, in the following article, we will summarize all information from formulas, calculations and exercises related to the volume of rectangular boxes so that everyone can follow and apply.

What is a rectangular box?

A rectangular box is a spatial geometry with 6 rectangular faces. Among them, there are 2 faces that have no common edges called 2 opposite faces or base surfaces, and the remaining faces are called side faces.

Bạn đang xem: Cách tính thể tính hình hộp chữ nhật chính xác và dễ nhớ

Some properties of rectangular boxes:

• A rectangle has 12 edges, 8 vertices and 6 faces.

• The diagonals have 2 endpoints that are 2 opposite vertices of a rectangular box that converge at 1 point

• The areas of two opposite faces in a rectangular box are equal

• The perimeters of two opposite faces in a rectangular box are equal

Formula to calculate the volume of a rectangular box

The formula for calculating the volume of a rectangular box is to multiply the length of the bottom surface (long) by the width of the bottom surface (wide), then multiply by the height of the box.

The general formula is: Volume (V) = Length (long) * width (wide) * height (high), or V = drc = a*b*c. In there:

• V: volume of a rectangular box.

• a: length of rectangular box.

• b: width of rectangular box.

• h: height of rectangular box.

Some other ways to calculate the volume of a rectangular box

In addition to calculating according to the general formula, you can calculate the volume of a rectangular box in the following ways:

Method 1: How to calculate the total area of ​​three equal sides and edges

This formula is: V = 2(ab + ac + bc), where a and b are the length and width respectively, c is the height.

For example:

Given a rectangular box with length a = 5 cm, width b = 3 cm and height c = 4 cm.

We can calculate the volume by calculating the total area of ​​the equal sides and sides.

S = 2(a*b + a*4 + b*c) = 2(5*3 + 5*4 + 3*4) = 94 cm^3

Method 2: How to calculate volume when knowing the area of ​​the base of a rectangular box

If the base area (Sd) of the rectangular box is known, you can calculate one of the two remaining parameters such as a or b (length or width). With length and width being the two dimensions of the bottom surface, we have the formula Sd = a*b. Based on this formula, we can calculate and find the missing parameter.

Once you have determined all the necessary parameters, use the formula V = a*b*c (if you already know a, b and c) to calculate the volume of the rectangular box.

Method 3: Formula to calculate volume when knowing the perimeter of a rectangular block

If the perimeter (C) of the rectangular box is known, you need to know at least two of the remaining three parameters (a, b and c). Circumference C is calculated using the formula: C = 4a + 4b + 4c.

Once you have determined all the necessary parameters, use the formula V = a*b*c (if you already know a, b and c) to calculate the volume of the rectangular box.

Types of exercises on how to calculate the volume of a rectangular box and solution methods

For the topic of calculating the volume of a rectangular box, students will get acquainted with some of the following basic exercises:

Form 1: How to calculate the volume of a rectangular box when knowing the length, width and height.

For example: Let the rectangular box be 6cm long, 3cm wide and 2cm high. Calculate the volume of that shape.

Solution instructions:

The volume of a rectangular box is:

V = lxwxh

V = 6cm x 3cm x 2cm

V = 36cm^3

Form 2: Given the rectangular box’s volume, two corresponding dimensions, and ask to calculate the size of the remaining side.

For example: Calculate the width of a rectangular box with volume 240cm^3, length 8cm and height 5cm.

V = lxwx h240cm^3 = 8cm xwx 5cmw = 6cm

Form 3: Calculate the height of a rectangular box when knowing the two corresponding side sizes and volume

For example: Given a rectangular box, the volume is 420cm^3, length 14cm and width 3cm. Calculate the height of the image?

V = lxwx h420cm^3 = 14cm x 3cm x hh = 10cm

Form 4: How to calculate the volume of some rectangular boxes that are partially cut off.

For example: Let the rectangular box be 12cm long, 6cm wide and 3cm high if part of the box is cut off. What is the volume of the image?

V = lxwx hV = (12cm x 6cm x 3cm) – (4cm x 3cm x 3cm)V = 648cm^3 – 36cm^3V = 612cm^3

Form 5: Calculate the volume of a rectangular box when a circular hole is punched out of one of its flat surfaces.

For example: Given a rectangular box with length 10cm, width 8cm and height 6cm if a circular hole with radius 2cm is punched out of one of its planes. What is the volume of the image?

V = lxwx hV = (10cm x 8cm x 6cm) – (pi x 2cm^2 x 6cm)V = 480cm^3 – 75.4cm^3V = 404.6cm^3

Form 6:. How to calculate the volume of a rectangular box when one of its corners is cut off.

For example: Given a rectangular box with length 8cm, width 6cm and height 4cm if one of its corners is cut off. What is the volume of the image?

V = lxwx hV = (8cm x 6cm x 4cm) – (2cm x 2cm x 4cm)V = 192cm^3 – 16cm^3V = 176cm^3

Form 7: Calculate the volume of a number of irregular rectangular boxes with planes that are offset from each other.

For example: Given an irregular rectangular box with length 10cm, width 5cm and height 4cm. The bottom plane of the box is an equilateral triangle with sides 6cm. Calculate the volume of the figure.

V = lxwx hV = (10cm x 5cm x 4cm) + (1/2 x 6cm x 4cm)V = 200cm^3 + 12cm^3V = 212cm^3

See more: Formula for calculating the volume of a cube & detailed solution instructions

Basic to advanced exercises for calculating the volume of rectangular boxes

Based on the above knowledge, below Nguyễn Tất Thành will synthesize some related exercises from basic to advanced so that you can apply and solve the exercises!

Exercises on calculating the volume of basic rectangular boxes

Problem 1: A rectangular box has a length of 8 m, a width of 5 m and a height of 6 m. Calculate the diagonal of a rectangular box.

Lesson 2: A water reservoir has a rectangular shape with a volume of 3000 m3, a width of 10 m and a height of 12 m. Calculate the length of the lake.

Exercise 3: Given a rectangular box with a length of 2.5cm, a width of 1.8cm and a height of 2cm. Calculate the volume, surrounding area, and total area of ​​that rectangular box.

Exercise 4: Given a rectangular box ABCD.A’B’C’D’ with base area SABCD = 24cm2 and volume V = 84 cm3. What is the height of the rectangular box?

Lesson 5: Calculate the volume of cube ABCD.A’B’C’D’, knowing that AA’B’D’ is a regular tetrahedron of side a.

Lesson 6: A rectangular water tank is 2m long. Initially the tank had no water. After pouring into the tank 120 barrels of water, each containing 20 liters, the water level of the tank is 0.8m.

a) Calculate the width of the water tank.

b) People poured 60 more barrels of water into the tank to fill the tank. How many meters high is the tank?

The exercises apply the advanced formula for calculating the volume of a rectangular box

In the 8th and 12th grade programs, children will expand their knowledge about planes. Therefore, in addition to calculating the volume of a rectangular box, students will get acquainted with the math methods of determining maximum/minimum volume, comparing the volume of two boxes and practical application problems.

Lesson 1: Given a rectangular box with dimensions proportional to 3; 4; 5 and the volume of the box is 60cm3. Calculate the maximum volume of that box.

Lesson 2: Cube A has equal sides

1212 sides of cube B. How much is the volume of cube A equal to the volume of cube B?

Lesson 3: A rectangular glass fish tank (no lid) is 1 m long, 70 cm wide, and 60 cm high. The water level in the tank is 30 cm high. If you put a stone in the tank, the volume increases by 14,000 cm3. How high is the water level in the tank now?

Answers to advanced exercises for calculating the volume of rectangular boxes

Lesson 1:

Xem thêm : Dạy trẻ cách phát âm chữ q trong tiếng Việt đơn giản mà hiệu quả ngay tại nhà

Call the dimensions of the given rectangular box a, b, c

Since the dimensions are proportional to 3; 4; 5 should:

a3=b4=c5=ta3=b4=c5=t

The volume of the box is:

V = abc so: 3t. 4 years old. 5t = 480

Deduce: 60t3 = 60 so t = 1

Therefore, a = 3cm; b = 4cm; c = 5cm

So the largest side of the box is 5cm

Lesson 2:

Call the length of one side of cube A a.

Because cube A has sides equal to 1212 edges of cube B, the length of one side of cube B is 2a

The volume of cube A is:

VA = a3.

The volume of cube B is:

VB = (2a)3 = 8a3

=> VB = 8VA

=> VA = 1818VB

So the volume of cube A is equal to 1818 the volume of cube B

Lesson 3:

Convert 1m = 100cm

The volume of the initial water tank is:

V = 100.70.30 = 210000 cm3

After adding a stone, the volume increases by 14000 cm3. So the volume of the water tank is then:

V1 = V + 14000

= 210000 + 14000 = 224000 cm3

Since the length and width of the water tank do not change, the change is due to the change in water level height. Call the subsequent water level height h cm. We have:

V = 100.70.h = 224000

=> h = = 32 cm

The secret to mastering how to calculate the volume V of a rectangular box

To help students learn this knowledge more easily and easily when solving math problems or applying it in practice, here are some experiences for everyone to refer to:

Grasp the basic knowledge of rectangular shapes

To solve the exercise on calculating the volume of a rectangular box, students are required to firmly grasp the knowledge related to this geometry, from concepts, properties, characteristics, calculation formulas and how to solve shapes. Corresponding exercises… Parents should take the time to guide their children to study and review their child’s old lessons, to know which part the child is having difficulty with, and then to reinforce and explain to avoid the situation. children “learn first and forget later”.

Practice regularly

Studying along with practice is a mandatory factor if you want to clearly understand the knowledge you have learned. Therefore, parents should encourage and ask their children to practice and do exercises on calculating the volume of rectangular boxes, or any other exercises more often. In addition, you can let your child participate in competitions, organize games, participate in mathematical activities… Thereby helping to stimulate the child’s thinking ability and mathematical ability better.

Create excitement when learning visual math with Nguyễn Tất Thành Math

Nguyễn Tất Thành Math is known as an online math teaching application for preschool and elementary school children, with content built closely to the Ministry’s latest educational program. This contributes to helping children both develop their math learning ability and support better results in school.

A special feature of Nguyễn Tất Thành Math is that it does not teach using the usual method of imparting knowledge, but instead applies active teaching methods such as through games, interactive activities, quizzes, and books. supplementary exercises… Thereby helping children easily gain interest and love when learning math.

At the same time, the lesson content on the application synthesizes a variety of topics from algebra to geometry, including the topic of rectangular boxes. All are divided into many levels from easy to difficult, personalized for each subject so that parents can easily choose the most suitable level for their child.

Make sure every hour of learning math with Nguyễn Tất Thành Math with your child is fun, as well as stimulating the child’s thinking ability and mathematical ability to develop more every day. To better understand the application, parents can refer to the following video, or register for free consultation.

Above is information to help people better understand how to calculate the volume of a rectangular box. This is knowledge that is not only applied in mathematics but also in many practical applications, so parents should refer to it for more information to guide their children to learn better. At the same time, if you don’t have much time or experience in teaching your child math, you can refer to the Nguyễn Tất Thành Math application.

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