115
The cuboid
Textbook: Part 4, lesson 115, pp. 22–24
GoalThe cuboid and the cube: faces, edges, vertices; the net and total surface area.
New words
cuboid · parallelepiped (kuboid)face · yoqedge · qirravertex · uch
Explanation
A cuboid and a cube both have 6 faces, 12 edges and 8 vertices. All faces of a cube are equal squares and all its edges are equal. Opposite faces of a cuboid are equal rectangles. A net is the whole surface of a solid laid out flat. The area of the net equals the total surface area of the solid. For a cuboid with length a, width b and height c the total surface area = 2 × (a × b + b × c + a × c).
Worked examples
A cube with edge 5 cm has total edge length 5 × 12 = 60 cm.
A 6 cm × 4 cm × 3 cm cuboid: 2 × (24 + 12 + 18) = 108 cm².
Class activity
“Box net”: with an adult's help, open out a matchbox or food box, count its faces and find which faces are equal.
Practice
1
What is the total length of all edges in cm of a cube with edge 5 cm?
60
2
What is the total surface area in cm² of a 6 cm × 4 cm × 3 cm cuboid?
108
3
The net of a cube is 6 squares with side 3 cm. What is its area in cm²?
54
4
What is the sum of the numbers of faces, edges and vertices of a cuboid?
26
5
An aquarium is 60 cm long, 30 cm wide and 40 cm high. What is the total area of its four side walls in cm²?
7200