The image shows different views of a cube made out of panels with cut-outs. Which option can be folded to make the given cube?
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To solve cube net problems, focus on two key checks: 1) Opposite Faces: In a valid net, faces that are separated by one other face in a straight line will be opposite each other on the cube. 2) Adjacency and Orientation: Pick a face as the "front" and mentally fold the adjacent faces up. Then, check if the orientation of the symbols matches the given 3D views.
Step 1: Understanding the Concept:
This is a classic spatial reasoning problem involving cube nets. We need to analyze the relationships (adjacency and orientation) between the faces of the cube shown in the 3D views and then determine which of the 2D nets (A, B, C, D) can be folded to reproduce these relationships.
Step 2: Detailed Explanation:
Let's establish the key adjacencies and orientations from the 3D views:
View 1: The triangle face is adjacent to the square cutout face and the star face. The apex of the triangle points towards the star face.
View 2: The square cutout face is adjacent to the circle cutout face and the face with two small circles.
View 3: The star face is adjacent to the triangle face and the circle cutout face.
From these views, we can deduce some key relationships:
The triangle, star, and square cutout faces meet at a vertex.
The star, circle cutout, and triangle faces meet at another vertex.
Now let's test each net by mentally folding it:
Net A: If we fold this net with the star as the front face, the triangle will be on the right and the square cutout will be on top. In this orientation, the triangle's apex points towards the top face (square cutout), which contradicts View 1 where the apex points towards the star face. So, A is incorrect.
Net B: Let's take the star as the front face. The face with two small circles will be the base. The square cutout face will be the top. The circle cutout face will be on the right. The triangle face will be on the left. Now let's check adjacencies.
The star is adjacent to the square cutout (top), circle cutout (right), triangle (left), and two small circles (bottom). This is consistent.
Let's check orientation. From View 1, the triangle's apex should point towards the star. In our fold of Net B, the triangle is on the left face. If we rotate the cube to see the triangle, star, and square cutout, their arrangement and the triangle's orientation will match the given views. All observed adjacencies can be formed from this net. So, B is correct.
Net C: In this net, the triangle and the circle cutout are opposite each other. However, View 3 shows them as adjacent faces. Therefore, C is incorrect.
Net D: If we fold this net, the orientation of the square cutout relative to the adjacent faces will be incorrect. For instance, if the face with two small circles is the base, and the circle cutout is the front, the square cutout will be on the left, but its orientation will not match the one seen in View 2. So, D is incorrect.
Step 3: Final Answer:
Only the net in option (B) can be folded to form the cube shown in the images.
