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 30?
- How many sticks are needed to make structure 185?
- A structure is made using 148 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 30
= 30 x 8 + 4
= 244
(b)
Number of sticks for structure 185
= 185 x 8 + 4
= 1484
(c)
Number of sticks = Structure number x 8 + 4
Structure number = (Number of sticks - 4) ÷ 8
Structure number for structure made with 148 sticks
= (148 - 4) ÷ 8
= 144 ÷ 8
= 18
Answer(s): (a) 244; (b) 1484; (c) 18
