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To reinforce understanding and application of the volume of a cube formula, students should complete additional exercises 1, 2, 3 in the textbook. For a clear demonstration of how to solve them correctly, students can refer to the solution guide in the document Solving 5th-grade math on pages 36 and 37 of VBT volume 2, Cubic Volume, Exercise 115.
Solving 5th-grade math on pages 36 and 37 of VBT volume 2, Cubic Volume, Exercise 115
1. Solve exercise 1 - Math exercise book for 5th grade volume 2 page 36
Question:
Fill in the blank with the appropriate measurement:
Solution Method
Apply the following formulas:
- Area of one face = side x side.
- Total surface area = area of one face x 6.
- Volume = side x side x side.
Answer
Given the side of the cube is 2.5m.
Surface area of one face of the cube:
S = 2.5 ⨯ 2.5 = 6.25 (m2)
Total surface area of the cube:
Stp = 6.25 ⨯ 6 = 37.5 (m2)
Volume of the cube:
V = 2.5 ⨯ 2.5 ⨯ 2.5 = 15.625 (m3)
Given the side of the cube is 3/4 dm.
Surface area of one face of the cube:
3/4 x 3/4 = 9/16 (dm2)
Total surface area of the cube:
9/16 x 6 = 27/8 (dm2)
Volume of the cube:
3/4 x 3/4 x 3/4 = 27/64 (dm3)
Given the side of the cube is 4cm.
Surface area of one face of the cube:
Surface area of one face of the cube:
16 ⨯ 6 = 96 (cm2)
Volume of the cube:
4 ⨯ 4 ⨯ 4 = 64 (cm3)
Volume of the cube:
5 ⨯ 5 ⨯ 5 = 125 (dm3)
Surface area of one face of the cube:
25 ⨯ 6 = 150 (dm2)
Total surface area of the cube:
150 (dm2)
Volume of the cube:
125 (dm3)
2. Solve exercise 2 - Math exercise book for 5th grade volume 2 page 36
Question:
A rectangular box has a length of 2.2m, a width of 0.8m, a height of 0.6m, and a cube with a side length equal to the average of the length, width, and height of that rectangular box.
a. Calculate the volume of each shape.
b. Which shape can have a larger volume and by how many cubic meters?
Solution Method
- Calculate the length of the cube side = (length + width + height) ÷ 3
- Calculate the volume of the rectangular box: V = length x width x height.
- Calculate the volume of the cube: V = side x side x side.
- Compare the volumes of the two shapes and find the difference between those volumes.
Answer
a. The volume of the rectangular box is:
The volume of the rectangular box is:
The side length of the cube is:
Volume of the cube is:
a. Calculate the volume of each shape.
1.728m³ > 1.056m³
Therefore, the volume of the cube is greater than the volume of the rectangular box and greater than the cubic meters by:
0.672m³ = 672dm³
Answer: a) Rectangular box: 1.056m³; Cube: 1.728m³; b) 672dm³.
672dm³
Answer: a) Rectangular box: 1.056m³; Cube: 1.728m³
b) 672dm³.
3. Solve Exercise 3 - Math Exercise Book for 5th Grade Volume 2 Page 37
Metal Cube Weight Calculation:
A metal cube with a side length of 0.15m. Each cubic meter of that metal cube weighs 10kg. How much does the metal cube weigh in kilograms?
Solution Method
- Calculate the volume of the metal cube by multiplying the side length by itself and then by itself again.
- Convert the volume obtained to cubic meters.
- Calculate the weight of the metal cube by multiplying the weight of each cubic meter of metal with the volume of the metal cube (in cubic meters).
Answer
The volume of the metal cube is:
0.15 ⨯ 0.15 ⨯ 0.15 = 0.003375 (m3)
0.003375m3 = 3.375dm3
The weight of the metal cube is:
10 ⨯ 3.375 = 33.75 (kg)
Answer: 33.75kg
You are viewing the guide for solving Grade 5 math problems on pages 36 and 37 of VBT Workbook 2: Volume of a Cube, Exercise 115. You can revisit the instructions for solving Grade 5 math problems on pages 34 and 35 of VBT Workbook 2: Volume of a Rectangular Prism or preview the instructions for solving Grade 5 math problems on pages 37 and 38 of VBT Workbook 2: Concentrated Practice to better understand the lesson.
Wishing you all success in your math studies.
