6. In the figure, you see a wire model of a $2 \times 2 \times 2$ cube consisting of 8 smaller cubes with edges of $1 \mathrm{dm}$. In total, the figure uses $54 \mathrm{dm}$ of wire. How many dm of wire is needed for a wire model of a $10 \times 10 \times 10$ cube consisting of a thousand smaller cubes with edges of $1 \mathrm{dm}$?
A) 121
B) 1000
C) 1210
D) 3000
E) 3630

![](https://cdn.mathpix.com/cropped/2024_04_17_227837a5972cf599de5fg-2.jpg?height=289&width=280&top_left_y=158&top_left_x=1573)
A6. E) 3630 Consider a wire model of a $10 \times 10 \times 10$ cube. First, we count the wires that go from front to back. These form 11 rows of 11 wires, so there are $11 \times 11=121$ wires that go from front to back. There are also 121 wires that go from left to right and 121 wires that go from top to bottom. Each of these wires has a length of $10 \mathrm{dm}$. The total length of the wires is therefore $3630 \mathrm{dm}$.