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 26?
- How many sticks are needed to make structure 144?
- A structure is made using 332 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 26
= 26 x 8 + 4
= 212
(b)
Number of sticks for structure 144
= 144 x 8 + 4
= 1156
(c)
Number of sticks = Structure number x 8 + 4
Structure number = (Number of sticks - 4) ÷ 8
Structure number for structure made with 332 sticks
= (332 - 4) ÷ 8
= 328 ÷ 8
= 41
Answer(s): (a) 212; (b) 1156; (c) 41