Figure P shows an isometric view of an object made with a single sheet of cardboard. Figure Q shows the front view of the same object after colouring. Which option shows the object after it is cut open?
Show Hint
In net-folding problems with color, first identify which faces of the 3D object are colored. Then, in the unfolded net, locate those same faces. The key is to understand how adjacency and orientation change when moving from a 2D net to a 3D object.
Step 1: Understanding the Concept:
This is a complex spatial visualization problem. We are given an object's 3D view (P) and its colored front view (Q). We need to determine the correct 2D unfolded pattern (net) that corresponds to this object, including the correct placement of the color. The coloring was applied to the folded object, and then it was cut open.
Step 2: Detailed Explanation: 1. Analyze the 3D Shape and Front View:
Figure P shows a trough-like structure with two vertical side panels and two diagonal inner panels forming an 'M' shape in cross-section.
Figure Q, the front view, shows the shape of the visible surfaces from the front. The fact that it's entirely green means all front-facing surfaces were colored. These are the two vertical panels and the two diagonal panels.
2. Analyze the Net:
The options show the net (the single sheet of cardboard, cut open and laid flat). The shape of the net itself is complex, resembling a cruciform (cross shape). The lines represent fold lines.
The question is to identify which coloring pattern on the net is correct. The green areas on the net must be the ones that, when folded, form the front of the object. All other surfaces (back, bottom, sides) should be white.
3. Mental Folding and Matching:
We must mentally fold the net from the options to see what 3D shape it creates and which surfaces face the front.
The central hexagonal and rectangular parts of the net likely form the base and back of the structure.
The four complex "arms" of the cross must fold up and inwards to form the front and sides of the structure shown in P.
Option A shows the entire arms colored green. If folded, this would likely make the sides of the structure green as well, which contradicts the information from the front view Q (we only know the front is green).
Option C shows a specific pattern where only certain parts of the arms are green. These green parts are positioned such that when the arms are folded up and inward to form the 'M' cross-section, they would all align to face the front, creating the solid green appearance seen in Q. The white parts of the arms would form the non-visible side surfaces of the structure's interior walls.
Options B and D have coloring patterns that would not result in the solid green front view shown in Q when folded.
Step 3: Final Answer:
Visualizing the folding process, the coloring pattern in Option C is the only one that correctly places the green color on the surfaces that constitute the object's front face, matching the view in Q.
