Solving 5th-grade math problem on page 26 of VBT workbook, Volume 2, Surface area and total area of a cube, problem 107

Solving 5th-grade math problem on page 26 of VBT workbook, Volume 2, Surface area and total area of a cube, problem 107, is a helpful math resource for students. Through this, students can easily and effectively solve exercises 1, 2, 3 as well as understand how to apply formulas for the surface area and total area of a cube into problems.

1. Solve exercise 1 - Math exercise book grade 5 volume 2 page 26

Problem:

Fill in the blanks appropriately:

a. The surface area of a cube with a side length of 2.5m is: ...

b. The total area of a cube with a side length of 2.5m is: ...

Solution Method

The surface area of a cube equals the area of one face multiplied by 4.

The total area of a cube equals the area of one face multiplied by 6.

Answer

a. Surface area of a cube with a side length of 2.5m is:

(2.5 ⨯ 2.5) ⨯ 4 = 25 (m²)

b. Total area of a cube with a side length of 2.5m is:

(2.5 ⨯ 2.5) ⨯ 6 = 37.5 (m²)

Fill in the blanks with appropriate measurements:

- The surface area of a cube equals the area of one face multiplied by 4.

- The total area of a cube equals the area of one face multiplied by 6.

- The area of one face equals the total area divided by 6.

- If there exists a number a such that the area of one face equals a x a, then the length of the side of the cube is a.

+) We have: 4 x 4 = 16. Therefore, the side length of the cube with an area of one face of 16cm² is 4cm.

The total surface area of the cube with an area of one face of 16cm² is:

16 x 6 = 96 (cm²)

+) The area of one face of a cube with a side length of 10cm is:

10 x 10 = 100 (cm²)

The total surface area of a cube with an area of one face of 100cm² is:

100 x 6 = 600 (cm²)

+) The area of one face of a cube with a total surface area of 24cm² is :

24 : 6 = 4 (cm²)

We have: 2 x 2 = 4. Therefore, the side length of the cube with an area of one face of 4cm² is 2cm.

So, we have the result table as follows:

a. The first cube has a side length of 8cm, and the second cube has a side length of 4cm. Calculate the surface area of each cube.

b. How many times is the surface area of the first cube greater than the surface area of the second cube?

- The surface area of a cube equals the area of one face multiplied by 4.

- To find how many times the surface area of the first cube is greater than the surface area of the second cube, divide the surface area of the first cube by the surface area of the second cube.

a. Cube a)

Area of one face of the cube:

8 ⨯ 8 = 64 (cm²)

Surface area of the cube:

64 ⨯ 4 = 256 (cm²)

- Cube b)

Area of one face of the cube:

4 ⨯ 4 = 16 (cm²)

Surface area of the cube:

16 ⨯ 4 = 64 (cm²)

b. The surface area of cube a) is how many times greater than cube b)?

256 : 64 = 4 (times)

You are watching the tutorial for solving math problems in Grade 5, page 26, Exercise 2: Surface Area and Total Surface Area of a Cube, Problem 107. You can review the tutorial for Grade 5, pages 24, 25, and 26, Exercise 2: Practice, or preview the tutorial for Grade 5, page 27, Exercise 2: Practice to understand more about the lesson.

Wishing you all the best in studying mathematics.