The following is a sequence of structures made by joining identical cubes with 1-cm sticks as edges.
- How many sticks are needed to make structure 90?
- How many sticks are needed to make structure 154?
- A structure is made using 228 sticks. Which structure is it?
(a)
Pattern for the number of sticks
Structure 1: 1 x 8 + 4= 12
Structure 2: 2 x 8 + 4 = 20
Structure 3: 3 x 8 + 4 = 28
Formula
Number of sticks = Structure number x 8 + 4
Number of sticks for structure 90
= 90 x 8 + 4
= 724
(b)
Number of sticks for structure 154
= 154 x 8 + 4
= 1236
(c)
Number of sticks = Structure number x 8 + 4
Structure number = (Number of sticks - 4) ÷ 8
Structure number for structure made with 228 sticks
= (228 - 4) ÷ 8
= 224 ÷ 8
= 28
Answer(s): (a) 724; (b) 1236; (c) 28
