Question:
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 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?
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Optimal cutting strategies involve reducing the number of cuts by planning cuts that simultaneously shorten multiple lengths.
Updated On: Apr 8, 2025
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The Correct Option is B
Solution and Explanation
Given a 12 m long wire and a cube with each edge measuring 1 m, the wire must be divided into 12 pieces, each 1 m long.
Step 1: Each 1 m piece corresponds to one edge of the cube.
Step 2: If we are to minimize the number of cuts, strategically:
Make 1 cut to get 2 pieces of 6 m each.
Cut each 6 m piece into two 3 m pieces (2 cuts total so far).
Finally, cut each 3 m piece into three 1 m pieces (4 cuts in total, as each 3 m cut into three 1 m pieces adds 2 cuts).
Step 3: This method requires a total of 4 cuts. Therefore, the minimum number of cuts required is 4.
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