2. Jacob cuts a square pyramid along the edges. What shapes does he now make and how many of each shape are there?
To determine the shapes created when Jacob cuts a square pyramid along the edges, we first need to understand the structure of a square pyramid. A square pyramid has a square base and four triangular faces that converge at a single point called the apex.
When Jacob cuts the square pyramid along the edges, the resulting shapes will depend on how he cuts it. Let's consider the possible scenarios:
1. If Jacob cuts the square pyramid parallel to the base along one of its triangular faces, he will create two shapes:
- A smaller square pyramid that is similar to the original pyramid with all its dimensions reduced.
- A rectangular prism formed by the removed triangular face and the portion of the original pyramid above it.
2. If Jacob cuts the square pyramid along the apex, he will also create two shapes:
- A smaller square pyramid without its apex. This new pyramid has a reduced height compared to the original pyramid.
- An isosceles triangular prism formed by the removed apex and the base of the original pyramid.
Therefore, the possible shapes that Jacob may create are:
- Smaller square pyramid
- Rectangular prism
- Smaller isosceles triangular prism
Since there can be different ways to cut the pyramid, the exact number of each shape generated will vary depending on Jacob's choice of cuts.