88
The net of a cuboid
Textbook: Part 3, lesson 88, pp. 61–63
GoalThe net of a cuboid is made of 6 rectangles; finding the total surface area.
New words
net · yoyilmaopposite faces · qarama-qarshi yoqlartotal surface · to‘la sirtpair · juft
Explanation
The net of a cuboid is made of 6 rectangles. The faces form three pairs, and the opposite faces in each pair are equal. If the length is a, width b and height c, the faces are a × b (2 of them), a × c (2) and b × c (2). To find the total surface area, double the area of each pair’s face and add the three results.
Worked examples
a = 6 dm, b = 4 dm, c = 5 dm: 6 × 4 × 2 = 48; 6 × 5 × 2 = 60; 4 × 5 × 2 = 40; S = 48 + 60 + 40 = 148 dm².
a = 3 cm, b = 2 cm, c = 1 cm: 6 × 2 + 3 × 2 + 2 × 2 = 12 + 6 + 4 = 22 cm².
Class activity
“Box net”: children carefully unfold a matchbox, colour the 6 rectangles in pairs, measure and calculate the areas.
Practice
1
A cuboid is 6 cm long, 3 cm wide and 2 cm high. What is its total surface area in cm²?
72
2
A cuboid measures 10 cm, 5 cm and 4 cm. What is its total surface area in cm²?
220
3
A box is 14 cm long, 6 cm wide and 8 cm high. What is the sum of the areas of its bottom and lid in cm²?
168
4
A box is 8 cm long, 5 cm wide and 2 cm high. What is the sum of the areas of its 4 side faces in cm²?
52
5
The lid of an aquarium is 50 cm long and 18 cm narrower than it is long. What is the lid’s area in cm²?
1600