Question

Given below is a drawing on a sheet of paper. Make a cut along the solid arcs and fold the resulting semicircular rings at 90 degrees along the dotted lines. What is the number of raised semicircular rings after following these steps?

Hint:

Each ring is the strip of paper trapped between two neighbouring cut arcs. So instead of counting the raised rings directly, count how many arc lines are drawn in the figure and subtract one - that count always equals the number of strips, and therefore the number of rings, between them.

Answer 1

Correct Answer: 5

Step 1: Analyze the drawing.
The drawing shows several semicircular rings arranged in a sequence. The task is to make cuts along the solid arcs and fold the resulting semicircular rings at 90 degrees along the dotted lines.
Step 2: Count the rings.
After making the cuts and folding along the dotted lines, each of the semicircular rings will be raised at a 90-degree angle. By observing the drawing carefully, we see that there are 5 raised semicircular rings after following the steps.
Step 3: Conclusion.
Therefore, the total number of raised semicircular rings after following the steps is \( \boxed5 \).

Answer 2

Concept:

• Each semicircular ring in the drawing is the strip of material trapped between two consecutive arc-shaped cut lines; that strip is what gets folded up along its inner dotted line.
• Instead of trying to identify and count "rings" directly, which is easy to double-count or miss at the edges, it is more reliable to count the concentric arc lines and use the fact that n arcs bound exactly (n - 1) strips between them.

Step 1: Count the concentric arc lines.
Starting from the innermost curve and moving outward to the outer boundary of the semicircular pattern, count every distinct arc drawn as a cut line. This gives 6 arc lines in total.

Step 2: Apply the boundaries-minus-one rule.
A ring is the material trapped between two neighbouring arcs, so the number of complete rings formed equals (number of arc lines) - 1.

Step 3: Compute the ring count.
Number of raised rings = 6 - 1 = 5.

Step 4: Confirm by the fold step.
After the cuts are made and each strip is folded upward at 90 degrees along its dotted fold line, every one of these 5 strips becomes a standing semicircular ring, since none of them are left flat.

Final Answer: 5