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Solving 7th-grade Math exercises on pages 66 and 67 from Volume 1 of the Creative Horizon textbook is a valuable resource for mastering the lesson on Exercises at the end of Chapter III following the textbook curriculum. Through this material, students can easily grasp the knowledge and tackle exercises 1, 2, 3... with ease.
Referencing various study materials for excelling in 7th-grade Math:
- Complete set of Solving 7th-grade Math problems from the Creative Horizon textbook
- Solving 7th-grade Math exercises on page 49 from Volume 1 of the Knowledge Connection textbook - Exercise 9: Parallel lines and identification signs
- Solving 7th-grade Math exercises on page 68 from Volume 1 of the Kite textbook - Exercise 8. Proportional quantities inverse relation
Solving 7th-grade Math exercises on pages 66 and 67 from Volume 1 of the Creative Horizon textbook
Exercises at the end of Chapter III
1. Solve Exercise 1 on Page 66 of 7th-grade Math textbook
Problem: A solid consists of 14 cubes attached to each other as shown in Figure 1. Each cube has a side length of 1 cm. Calculate the volume of this solid.
Problem: A rectangular fish tank with dimensions of the base being 5 dm and 12 dm, has a water level of 7 dm. When pouring a certain amount of sand (with negligible water permeability), the water level rises by an additional 1.5 dm and the sand is submerged. Calculate the volume of the sand.
Guidance on solving:
+ Calculate the initial volume of water.
+ Calculate the volume of water and sand after pouring sand.
+ Calculate the volume of sand poured = volume of water and sand after pouring sand - initial volume of water.
Calculate the length, width, and height of the core mold.
The volume of the concrete block cast with this mold = volume of the core mold.
Answer:
The length of the core mold is:
23 - 1.2 - 1.2 = 20.6 (cm)
The width of the core mold is:
13 - 1.2 - 1.2 = 10.6 (cm)
The height of the core mold is:
11 - 1.9 = 9.1 (cm)
The volume of the concrete block cast with this mold is:
V = 20.6 × 10.6 × 9.1 = 1987.076 (cm³)
4. Solve Problem 4 on Page 66 Math Textbook Grade 7
Given the inner part of a baking mold shaped like a rectangular box with a square base measuring 20 cm on each side and a height of 5 cm (Figure 3). It is planned to paint the inner part with a non-stick paint. How many baking molds can be painted with enough paint to cover an area of 100 m²?
Calculate the area of the inner part of the mold: A = Aside + Abase.
Number of baking molds = area covered : area of 1 mold.
Answer: The number of baking molds that can be painted is...
Answer:
Area of the inner part of the mold:
S = (4 * 20) * 5 + 20 * 20 = 800 (cm²)
Convert 800 cm² to 0.08 m²
The number of painted baking molds is:
100 : 0.08 = 1250 (units)
5. Solve Problem 5 Page 66 Mathematics Textbook Grade 7
Problem: A house has dimensions as shown in Figure 4.
a) Calculate the volume of the house.
b) Knowing that 1 liter of paint covers 4 m² of wall. How many liters of paint are needed to cover the outer walls of the house? (excluding doors) Given that the total area of the doors is 9 m².
Instructions:
Divide the house into a rectangular prism and a triangular prism.
a) Volume of the house = volume of rectangular prism + volume of triangular prism.
b) Area to be painted = surface area of rectangular prism + area of 2 bases of the triangular prism - area of doors
Answer:
Divide the house into a rectangular prism with a base length of 20 m, width 15 m; height 8 m and a triangular prism with a base length of 15 m, corresponding height is 15 - 8 = 7 (m).
The volume of the house is:
V = 20 * 15 * 8 + 15 * 7 * 20 = 4500 (m³)
The area to be painted is:
The minimum amount of paint needed to cover the outer walls of the house is:
2496 : 4 = 624 (liters)
6. Solve Problem 6 Page 67 Mathematics Textbook Grade 7
Problem: The rectangular prisms in Figure 5 have the same volume. Find the missing dimensions.
Instructions:
Step 1: Calculate the volume of the rectangular prism = length x width x height.
Step 2: Find the missing dimensions in the shapes.
Answer:
The volume of each rectangular prism is:
V = 2 * 12 * 12 = 288 (cm³).
Considering figure 5a: The height of the rectangular prism is: 288 : 8 : 8 = 4.5 (cm).
Considering figure 5b: The height of the rectangular prism is: 288 : 4 : 4 = 18 (cm).
Considering figure 5c: The side length of the base of the rectangular prism is: 288 : 8 : 6 = 6 (cm).
Considering figure 5d: The height of the rectangular prism is: 288 : 12 : 9 = 8/3 (cm).
7. Solve Problem 7 Page 67 Mathematics Textbook Grade 7
Problem: Construct a vertical prism with a height of 2.5 cm, a base in the shape of a rhombus with a side length of 3 cm, and an angle of 60 degrees.
Instructions:
Determine the lengths of the edges, shapes of the faces of the prism.
Draw the figure on paper, cut and fold as required by the problem.
Answer:
Step 1: Draw 4 rectangles with dimensions 3 cm x 2.5 cm and two rhombuses with side length 3 cm, with 1 angle of 60 degrees (as shown below).
Step 2: Cut the cardboard piece as shown in the drawing and fold along the dashed lines, we get the vertical prism with a height of 2.5 cm, a rhombus base with a side length of 3 cm and an angle of 60 degrees.
8. Solve Problem 8 Page 67 Mathematics Textbook Grade 7
Problem: Describe the steps to create a triangular vertical prism in Figure 6.
Instructions:
Observe the drawing, describe the steps to create the prism.
Answer:
Step 1: Draw 3 rectangles with dimensions of 15 cm x 5 cm; 15 cm x 12 cm; 15 cm x 13 cm and two right-angled triangles with side lengths of 5 cm and 12 cm (as shown below).
Step 2: Fold the edges along the dashed lines to obtain the triangular vertical prism in Figure 6.
9. Solve Problem 9 Page 67 Mathematics Textbook Grade 7
Problem: A piece of cardboard is cut to create a vertical prism with an equilateral triangle base as shown in Figure 7. Determine the lengths of the base edges and the height of the vertical prism.
Instructions:
The edges that are not the base edges are the lateral edges of the vertical prism.
The length of the lateral edge of the vertical prism is the height.
Answer:
We observe that the base of the prism is an equilateral triangle with a side length of 3 cm.
The lengths of the base edges are 3 cm.
The height of the prism is 7 cm.
Here, Mytour has guided Grade 7 Math solutions on pages 66, 67 of Creative Horizon Textbook Volume 1, hoping that the exercises from the end of Chapter 3 become easier for students.
References:
- Grade 7 Math solutions on page 72 of Creative Horizon Textbook Volume 1 - Exercise 1: Special position angles
- Grade 7 Math solutions on page 75 of Creative Horizon Textbook Volume 1 - Exercise 2: Bisectors of angles
