The figure shows a series of steps built using square cubes. The n number of steps is given by x -step.
- How many square cubes were used if n is 8?
- How many square cubes were used if n is 34?
- Find the number of steps if a total of 64 cubes are used.
Figure
number |
Number of
square cubes |
Area
(cm2) |
Perimeter
(cm) |
| 1 |
1 |
4 |
8 |
| 2 |
3 |
12 |
16 |
| 3 |
6 |
24 |
24 |
| 4 |
10 |
40 |
32 |
| 8 |
(a) |
... |
... |
(a)
Pattern for the number of square cubes
1-step: 1 = 1
2 = 1
2-step: 1 + 3 = 2
2 = 4
3-step: 1 + 3 + 5 = 3
2 = 9
Number of square cubes = Step number
2 Number of square cubes for 8-step
= Sum of odd numbers
= Step number
2 = 8
2 = 64
(b)
Number of square cubes for 34-step
= Sum of odd numbers
= Step number
2 = 34
2 = 1156
(c)
Number of square cubes = Step number
2 Number of steps = √Number of square cubes
Number of steps for 64 square cubes
= √64
= 8
Answer(s): (a) 64; (b) 1156; (c) 8
