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Detailed solutions for exercises 1, 2, 3 of Grade 5 Math Problem Solving Pages 23, 24 VBT Book 2, Exercise 105.
Grade 5 Math Problem Solving Pages 23, 24 VBT Book 2, Surface Area and Total Area of Rectangular Prism, Exercise 105
Solve Exercise 1 - Grade 5 Math Exercise Book 2 page 23
Problem Statement:
Fill in the blank with the appropriate measurement:
Solution Method:
- To find the surface area of a rectangular prism, multiply the perimeter of the base by the height (using the same unit of measurement).
- To calculate the total surface area of a rectangular prism, add the lateral surface area to the area of two bases.
Answer
+) Rectangular prism (1):
The perimeter of the base of shape (1) is: (8 + 5) x 2 = 26 (dm)
The lateral surface area of shape (1) is: 26 x 4 = 104 (dm2)
The area of one base of shape (1) is: 8 x 5 = 40 (dm2)
The total surface area of shape (1) is: 104 + 40 x 2 = 184 (dm2)
+) Rectangular prism (2):
The perimeter of the base of shape (2) is: (1.2 + 0.8) x 2 = 4 (m)
The lateral surface area of shape (2) is: 4 x 0.5 = 2 (m2)
The area of the base of shape (2) is: 1.2 x 0.8 = 0.96 (m2)
The total surface area of shape (2) is: 2 + 0.96 x 2 = 3.92 (m2)
So we have the following result table:
2. Solve problem 2 - Math workbook grade 5 volume 2 page 23
Problem:
A rectangular tin box without a lid has a length of 1.2m, a width of 0.8m, and a height of 9dm. Calculate the area of tin required to make the box (excluding the welded edge).
Solution Method
Since the box has no lid, the area of tin used to make the box is the sum of the lateral surface area of the tin box and the base area of the tin box.
Answer
Convert: 9dm = 0.9m
The perimeter of the base of the tin box is:
(1.2 + 0.8) x 2 = 4 (m)
The lateral surface area of the tin box is:
4 x 0.9 = 3.6 (m2)
The area of the base of the tin box is:
1.2 x 0.8 = 0.96 (m2)
The area of tin required to make the box is:
3.6 + 0.96 = 4.56 (m2)
Answer: 4.56 square meters.
3. Solve problem 3 - Math workbook grade 5 volume 2 page 24
Problem:
Write 'equal' or 'not equal' appropriately in the blank:
a. Surface area of the two rectangular boxes ..........................
b. Total surface area of the two rectangular boxes .....................
Solution Method
- Calculate the surface area and total surface area of each box, then compare the results.
- To find the lateral surface area of a rectangular prism, multiply the perimeter of the base by the height (using the same unit of measurement).
- To calculate the total surface area of a rectangular prism, add the lateral surface area to the area of two bases.
Answer
- Figure a)
The perimeter of the base of the rectangular box is:
(1.5 + 0.8) x 2 = 4.6 (m)
The lateral surface area of the rectangular box is:
4.6 x 1 = 4.6 (m2)
The area of the base of the rectangular box is:
1.5 x 0.8 = 1.2 (m2)
The total surface area of the rectangular box is:
4.6 + 2 x 1.2 = 7 (m2)
- Figure b)
The perimeter of the base of the rectangular box is:
(0.8 + 1) x 2 = 3.6 (m)
The lateral surface area of the rectangular box is:
The lateral surface area of the rectangular box is:
The area of the base of the rectangular box is:
0.8 x 1 = 0.8 (m2)
The total surface area of the rectangular box is:
5.4 + 2 x 0.8 = 7 (m2)
a. The lateral surface area of the two rectangular boxes is not equal.
b. The total surface area of the two rectangular boxes is equal.
You are currently viewing the guide for solving math problems for Grade 5, page 23, 24 in the Exercise Book Volume 2: Surface Area and Total Surface Area of Rectangular Boxes, Exercise 105. You can review the guide for solving math problems for Grade 5, page 22, 23 in the Exercise Book Volume 2: Rectangular Boxes. Cubes or preview the guide for solving math problems for Grade 5, page 24, 25, 26 in the Exercise Book Volume 2: Practice to understand more about the lesson.
Best wishes for your math studies!
