Shown in the figure are pages in a children's book with holes in it. The book is cut along the red line. Which option shows the correct cross section?
Show Hint
When solving cross-section problems, systematically trace the cutting line across each part of the object. Pay close attention to the relative sizes of the features (like holes or solid parts) that the line intersects.
Step 1: Understanding the Concept:
The question asks us to visualize the cross-section of a book with die-cut holes. A cross-section shows what the object looks like at the point where it is sliced. In this case, we will see solid parts (the paper) and empty parts (the holes).
Step 2: Detailed Explanation:
We must trace the red cutting line from left to right and determine what it passes through at each section of the book.
Front Cover: The line passes through the paper, then through the circular hole, and then through the paper again. The cross-section should show `paper - gap - paper`.
Pages 1-4: The line passes through the paper, then through the large irregular hole, and then through the paper. The cross-section should show `paper - large gap - paper`.
Pages 5-8: The line passes through the paper, then through the oval hole, and then through the paper. This hole is narrower along the red line than the hole in pages 1-4. The cross-section should show `paper - medium gap - paper`.
Pages 9-12: The line passes entirely through the paper in this section. There is no hole along the cutting line. The cross-section should be a `solid block of paper`.
Back Cover: The line passes through the paper, then through the hole on the right, and then through the paper. The cross-section should show `paper - gap - paper`.
Now let's compare this sequence with the options.
Option A and D: Both incorrectly show a gap in the section for pages 9-12, which should be solid.
Option B: It shows the gap for pages 1-4 as smaller than the gap for pages 5-8, which is incorrect. The diagram clearly shows the hole in pages 1-4 is wider along the red line.
Option C: This option correctly shows the sequence: a gap in the front cover, a large gap in pages 1-4, a smaller gap in pages 5-8, a solid section for pages 9-12, and a gap in the back cover. This matches our analysis exactly.
Step 3: Final Answer:
Option C is the only one that shows the correct cross-section of the book along the red line.
