GATE 2024 ME – Question 9
A planar rectangular paper has two V-shaped pieces attached as shown below.
[Figure: A long horizontal paper strip with a V-shaped chevron piece attached above its left end and a second V-shaped chevron piece attached below its left end.]
This piece of paper is folded to make the following closed three-dimensional object.
[Figure: A closed solid in the shape of a V, a bar of rectangular cross-section bent into two arms that meet at the bottom.]
The number of folds required to form the above object is
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Correct answer: (B) 7
Explanation
The solid is a V-shaped prism. Its two V-shaped faces are the two chevron pieces, and its side faces are six rectangles that run round the V (the two outer sides, the two inner sides and the two ends). The long strip supplies the six rectangles in a row, which takes 5 folds between neighbouring rectangles, and each chevron is folded onto the strip along one edge, which takes 2 more folds. That gives $5 + 2 = 7$ folds, which is one fewer than the 8 faces.