A hollow paper cone is cut by a spiral blade. The blade, the cone, the position of the cone and blade, and the line along which it gets cut are shown below. The surface of the cone is then unwrapped on a flat surface. Which option shows the unwrapped surface?
The problem involves visualizing and understanding how a hollow paper cone, when cut by a spiral blade, unfolds into a two-dimensional shape. To solve this, consider the geometrical properties of a cone.
A cone, when unwrapped, becomes a sector of a circle. The hollow space inside the cone means that this sector will form a spiral pattern. The key lies in identifying how the intersection takes place:
The cone's surface is divided into sections based on the spiral's pattern.
Each section of the spiral is separated by a cut that follows the spiral within the cone.
This cutting action transforms the surface from a three-dimensional form (cone) into a two-dimensional pattern (sector with spirals).
Considering this understanding, we need to identify which of the given options represents the correct flat pattern:
The correct option should show a pattern exhibiting the spiral cuts while maintaining the original circular sector form of the unpeeled cone surface. Examine the provided images. The image that shows a circled pattern with an outward coil that traces the original spiral path on the cone surface fits this description.
