Twelve Cubed
A wooden cube with edges of length 12cm is cut into cubes with edges of length 1cm. What is the total length of the all the edges of these centimetre cubes?
Age
14 to 16
Challenge level
Problem
A wooden cube with edges of length $12$cm is cut into cubes with edges of length $1$cm.
What is the total length of all the edges of all these centimetre cubes?
If you liked this question, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
In total there are $12\times12\times12$ or $12^3$ cubes with edge length $1$cm.
Each cube has twelve edges, so the sum of the lengths of the edges on one cube is $12$cm.
Therefore the total length of all the edges of all the centimetre cubes is $12^3\times12 = 12^4 = 20,736$cm