IMC 2007 Q16
16. A wooden cube with edge length 12 cm is cut into cubes with edge length 1 cm. What is the total length of all the edges of all these centimetre cubes?
- A 12 cm
- B 122 cm
- C 123 cm
- D 124 cm
- E 125 cm
Intermediate Mathematical Challenge 2007, Question 16. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 124 cm
In total, there are 123 cubes with edge length 1 cm. Each of these centimetre cubes has 12 edges, so the sum of the lengths of these edges is 12 cm. Therefore the total length of the edges of all the centimetre cubes is 123 × 12 cm, that is 124 cm.
Solution © UK Mathematics Trust, from the IMC 2007 solutions.