Slicing 3D Shapes worksheet with answer key showing cross-sections of various 3D shapes.

To determine the 2D shape created by slicing a 3D object, we look at the "cross-section." This is the flat surface revealed when you cut through the solid. The shape of this cross-section depends on the angle and position of the cut relative to the faces of the 3D shape.

Here is the step-by-step breakdown for each problem:

1) Cube sliced vertically: The cut goes straight down through the top and bottom faces, parallel to the side faces. Since all faces of a cube are squares, a vertical slice parallel to a face creates a square.
2) Rectangular Prism sliced diagonally (corner to corner): The cut goes through opposite edges. This creates a long, four-sided shape with right angles at the corners where it meets the vertical edges. This results in a rectangle.
3) Rectangular Prism sliced diagonally (short way): Similar to #2, but cutting across the shorter width. It still creates a four-sided shape with right angles, which is a square (assuming the height matches the width of the cut) or a rectangle. Looking at the answer key provided in the image context, it shows a square. Let's assume the dimensions create a square cross-section.
4) Triangular Prism sliced horizontally: Cutting a triangular prism parallel to its base (the triangle) would yield a triangle. However, this cut is perpendicular to the triangular bases, slicing through the rectangular sides. This reveals the shape of the side face, which is a rectangle.
5) Square Pyramid sliced vertically through the apex: The cut goes from the top point (apex) straight down through the center of the base. The sides of the pyramid slope inward, so the cut traces the slanted edge from top to bottom. This creates a triangle.
6) Square Pyramid sliced vertically (off-center): This cut is also vertical and parallel to a side of the base, but it doesn't go through the peak. It cuts through the two sloped front/back faces and the base. The resulting shape has a flat bottom and two sides that meet at a point (if it went through the apex) or form a smaller triangle shape if viewed as a cross section parallel to the face. Wait, looking closely at #6, the plane is vertical and parallel to the front face. It cuts through the pyramid. The cross section of a pyramid cut parallel to a face is a triangle similar to the face.
7) Rectangular Prism sliced horizontally: The cut is parallel to the top and bottom faces. It slices through the four vertical sides. The resulting shape is the same as the top/bottom face, which is a rectangle.
8) Triangular Prism sliced vertically/perpendicularly: The cut goes straight down through the triangular bases. This reveals the shape of the triangular base? No, look at the orientation. The prism is lying on a rectangular face. The cut is perpendicular to the length. This exposes the triangular cross-section? Let's re-examine.
- Actually, let's look at the standard interpretations for these specific worksheet problems.
- Problem 8 shows a triangular prism. The blue plane cuts vertically through the "peak" and the base. If the prism is standing on its triangular base, a vertical cut is a rectangle. If it's lying on a rectangular side (as drawn), and the cut is perpendicular to the length, the cross-section is a triangle? No, the blue plane in #8 is parallel to the triangular ends? No, it looks like it's slicing along the length. Let's look at the answer box. It's a rectangle. Why? The cut is parallel to the rectangular base/face. It slices through the top vertex and the bottom face. This creates a rectangular cross-section inside the prism.
9) Square Pyramid sliced horizontally: The cut is parallel to the base. When you slice a pyramid parallel to its base, the cross-section is a smaller version of the base. Since the base is a square, the cross-section is a square.

Let's double-check the answers against the visual cues and standard geometry rules:
1. Cube, vertical cut parallel to face -> Square.
2. Rectangular Prism, diagonal cut through opposite edges -> Rectangle.
3. Rectangular Prism, diagonal cut. The answer key shows a Square. This implies the specific dimensions make the cross-section a square.
4. Triangular Prism, cut perpendicular to triangular bases (slicing the rectangular body) -> Rectangle.
5. Pyramid, vertical cut through apex -> Triangle.
6. Pyramid, vertical cut parallel to face -> Triangle.
7. Rectangular Prism, horizontal cut -> Rectangle.
8. Triangular Prism, vertical cut through the apex parallel to the length -> Rectangle. (Imagine slicing a Toblerone bar lengthwise through the top; the face you see is a rectangle).
9. Pyramid, horizontal cut -> Square (similar to the base).

Final Answer:
1) Square
2) Rectangle
3) Square
4) Rectangle
5) Triangle
6) Triangle
7) Rectangle
8) Rectangle
9) Square