Which set of pieces can form a full circle, if rotation of pieces is not permitted?
Show Hint
In shape assembly puzzles, first check the fundamental geometry. To form a circle, all outer boundaries must be circular arcs of the same radius, and all inner vertices must meet at a single central point. All pieces must be true sectors.
Step 1: Understanding the Concept:
The question asks us to identify which set of four shapes can be assembled into a complete circle without rotating any of the individual pieces. This requires us to mentally translate the pieces to see if they fit together perfectly.
Step 2: Detailed Explanation:
A full circle is comprised of 360 degrees. We need to check if the pieces in each set can combine to form a continuous circular shape. Since rotation is not allowed, the pieces must fit in their given orientation.
Set A: The red piece is a sector of a circle. The blue piece is also a sector. The yellow piece is a triangle with a curved base. The green piece is a sector with a concave side. These pieces do not appear to have angles that would sum to 360 degrees, and their shapes are mismatched. For example, the straight edge of the yellow triangle cannot fit with the curved edge of the blue sector.
Set B: The shapes are slightly different from set A, but the same problem exists. The straight edges and curved edges do not align in a way that would form a circle. The yellow and green pieces are not simple sectors.
Set C: Again, we have a mix of shapes. The yellow and green pieces are not true sectors of a circle and will not fit with the red and blue sectors to form a perfect circle.
Set D: In this set, all four pieces (red, blue, yellow, and green) are perfect sectors of a circle. Each piece appears to be a 90-degree sector (a quadrant). If we place them together, their central angles will sum to \(4 \times 90^\circ = 360^\circ\). Their curved edges all have the same radius, and their straight edges will meet at the center. By translating them, we can see they will form a complete circle.
Step 3: Final Answer:
The set of pieces in option (D) can form a full circle without rotation.
