Q.4 A thin wire is used to construct all the edges of a cube of 1 m side by bending, cutting and soldering
the wire. If the wire is 12 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
✅ The correct answer is (A) 3
By folding the 12 m wire into layers and cutting smartly, you can obtain 12 pieces of 1 m each using only three cuts.
By folding the 12 m wire into layers and cutting smartly, you can obtain 12 pieces of 1 m each using only three cuts.
Problem Statement
A thin wire is used to construct all the edges of a cube of side 1 m by bending, cutting and soldering.
Total wire length available is 12 m.
Step-by-Step Solution
1
Total wire needed
Total wire needed
- A cube has 12 edges.
- Each edge is 1 m long (side of cube = 1 m).
- Total length required = 12 × 1 = 12 m, which matches the given wire length.
So the task is only about how to cut this 12 m wire most efficiently.
2
Naive cutting approachIf you simply want 12 separate pieces of 1 m each from a 12 m wire:
Naive cutting approachIf you simply want 12 separate pieces of 1 m each from a 12 m wire:
- To get n pieces from a single straight piece, you need n-1 cuts.
- Here, n=12, so cuts required = 12-1=11.
- But 11 is not among the options, which means you are expected to fold and cut multiple segments at once.
3
Optimal folding strategyStep 1: Fold the 12 m wire into three equal layers
Optimal folding strategyStep 1: Fold the 12 m wire into three equal layers
- Each part will be 12÷3=4 m long.
- Now you have a stack of 3 parallel layers, each 4 m long.
Step 2: Make three cuts across all layers
- Mark points at every 1 m along the 4 m length (at 1 m, 2 m, and 3 m).
- Cut once at each mark through all three layers simultaneously:
- Cut at 1 m → each 4 m layer becomes 1 m + 3 m
- Cut at 2 m → each 3 m segment becomes 1 m + 2 m
- Cut at 3 m → each 2 m segment becomes 1 m + 1 m
- Result: Each of the 3 layers gives 4 segments of 1 m each.
- Total pieces = 3×4=12 segments of 1 m.
Thus, with only 3 cuts, you obtain 12 pieces of 1 m each, enough to form all edges of the cube after bending and soldering.
Why Each Option Is Right or Wrong
🎯 Key Takeaways for Exams
- A cube has 12 equal edges; total wire = 12 m for 1 m side.
- Normally n-1 cuts needed unless multiple layers are cut simultaneously.
- Optimal: 3 layers × 4 m → 3 cuts = 12 pieces of 1 m.
- Minimum cuts = 3 ✓
