85
Total edge length of a cube
Textbook: Part 3, lesson 85, pp. 54–55
GoalThe total length of all edges of a cube: L = a × 12.
New words
cube · kubedge · qirrawire · simframe · karkas
Explanation
A cube has 12 equal edges. If an edge has length a, the total length of all edges is L = a × 12. A wire frame of a cube needs exactly this much wire. In the reverse problem we find the edge: a = L : 12.
Worked examples
Edge 9 cm: L = 9 × 12 = 108 cm.
If L = 240 cm, then a = 240 : 12 = 20 cm.
Class activity
“Wire frame”: children build a cube from sticks and plasticine and count how many sticks and joins (vertices) it took.
Practice
1
A cube has edge 6 cm. What is the total length of its edges in cm?
72
2
The total length of all edges of a cube is 600 cm. How many centimetres is one edge?
50
3
How many centimetres of wire are needed for a cube frame with edge 25 cm?
300
4
A wire is 2 m long. A cube frame with edge 15 cm was made from it. How many centimetres of wire are left?
20
5
A cube has edge 10 cm. Each edge is lengthened by 2 cm. By how many centimetres does the total edge length grow?
24