GATE Chemical 2025 | GA | Question: 4

Question

​​A thin wire is used to construct all the edges of a cube of $1 \: \mathrm{m}$ side by bending, cutting and soldering the wire. If the wire is $12 \: \mathrm{m}$ long, what is the minimum number of cuts required to construct the wire frame to form the cube?

• A. $3$
• B. $4$
• C. $6$
• D. $12$

Answer 1

• A cube has 12 edges. Since each edge of the cube is 1 m long, and the total wire length is 12 m, we need to divide the 12 m wire into 12 separate pieces, each 1 m long.
• First cut: Cut the 12 m wire into two 6 m pieces.
• Second cut: Stack the two 6 m pieces and cut them simultaneously at the 3 m mark (from one end) to get four 3 m pieces.
• Third cut: Stack the four 3 m pieces and cut them simultaneously at the 1 m mark (from one end) to get four 1 m pieces and four 2 m pieces.
• Fourth cut: Stack the four 2 m pieces and cut them simultaneously at the 1 m mark to get eight 1 m pieces. 

Answer 2

Constraints given in the question - 12 metres of wire, cube has perimeter 12 meters (12 edges of length 1 meter) ; no edge can be covered by the wire more than once else we'll run out of wire

4 pieces, 3 cuts

Try to make first piece as big as possible

1-6-12-7-5-11-3-2-10. 9 edges covered. 

3 edges remaining = 4, 8, 9. All 3 are disjoint from eachother; need seperate pieces for each.

4 distinct pieces, requiring three cuts on the wire (imagine wire has markings going from 0m at its base to 12m at its end, first cut = at 9m mark, second at 10, third at 11)