Rotated positions of a single solid are shown below. The various faces of the solid are marked with different symbols like dots, cross and line. Answer the three items (14-16) that follow the given figures.
What is the symbol on the face opposite to that containing the cross?
Correct Answer :
Line
Solution :
The correct option is Line.
To find the symbol on the face opposite to the one containing the cross, we can analyze the adjacent faces shown in the four positions of the solid:
1. In Figure (I), the top face contains a line, the front face contains one dot, and the right face contains two dots. This means the line is adjacent to the one dot face and the two dots face.
2. In Figure (II), the top face contains a line, the front face contains two dots, and the right face contains three dots. This means the line is adjacent to the two dots face and the three dots face.
3. In Figure (III), the top face contains a line, the front face contains three dots, and the right face contains four dots. This means the line is adjacent to the three dots face and the four dots face.
By combining these observations, we can identify all four faces that are adjacent to the face with the line:
- One dot (from Fig. I)
- Two dots (from Fig. I and II)
- Three dots (from Fig. II and III)
- Four dots (from Fig. III)
A cube has six faces in total. Any given face has exactly four adjacent faces and one opposite face. The six symbols featured on the faces of this solid are one dot, two dots, three dots, four dots, cross, and line (as shown in Figure (IV), which displays the cross face adjacent to two dots and one dot).
Since the four faces adjacent to the line are those with one, two, three, and four dots, the only remaining face that is not adjacent to it must be the cross. Therefore, the face opposite to the line is the cross, meaning the symbol on the face opposite to that containing the cross is the line.
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