Math worksheet for identifying 2D cross-sections from slicing 3D shapes.

It looks like you've uploaded an image of a worksheet titled "Slicing 3D Shapes" with an answer key already provided. The task is to determine the 2D cross-section that results when each 3D shape is sliced as shown by the blue plane.

Let’s go through each problem and explain why the given answer (the 2D shape below each 3D figure) is correct.

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🔷 1) Cube sliced vertically (parallel to face)

- Shape: Cube
- Slice: Vertical, parallel to one of the faces
- Cross-section: Square
✔ Answer: Square
➡️ When you slice a cube straight down through its center parallel to a face, the cross-section is a square — same as the face.

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🔷 2) Rectangular prism sliced diagonally

- Shape: Rectangular prism (like a box)
- Slice: Diagonal cut from top edge to bottom edge
- Cross-section: Rectangle
✔ Answer: Rectangle
➡️ Even though it's diagonal, if the cut goes through two opposite edges (and the plane is flat), the resulting shape is a rectangle, because the sides are straight and the angles remain right angles in projection.

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🔷 3) Rectangular prism sliced horizontally (top to bottom)

- Shape: Rectangular prism
- Slice: Horizontal cut through the middle
- Cross-section: Square
⚠️ Wait — this might be misleading.
Actually, the cross-section should be a rectangle, unless the height equals the width. But since the answer key says square, we assume the dimensions are such that the cross-section is a square.
✔ Answer: Square
➡️ If the cut is horizontal and the top/bottom face is a square, then yes — slicing parallel to the base gives a square.

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🔷 4) Triangular prism sliced horizontally

- Shape: Triangular prism (two triangular ends, rectangular sides)
- Slice: Horizontal cut across the middle
- Cross-section: Rectangle
✔ Answer: Rectangle
➡️ A horizontal slice through a triangular prism cuts through the three rectangular faces, forming a rectangle.

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🔷 5) Pyramid sliced vertically through apex

- Shape: Square pyramid
- Slice: Vertical cut through the apex and the base
- Cross-section: Triangle
✔ Answer: Triangle
➡️ Slicing through the tip (apex) and down through the base creates a triangle — the cross-section includes the apex and two points on the base.

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🔷 6) Pyramid sliced horizontally (parallel to base)

- Shape: Square pyramid
- Slice: Horizontal cut above the base
- Cross-section: Triangle
✘ Wait — this seems incorrect!
A horizontal slice parallel to the base of a pyramid should create a smaller square (similar to the base), not a triangle.

But the answer key says Triangle.

❗ This appears to be an error in the answer key.

👉 Correct cross-section for a horizontal slice of a square pyramid is a square, not a triangle.

However, looking at the diagram more closely:
The slice is not horizontal — it's diagonal, cutting through the pyramid from one side to another.

If the slice passes through the apex and cuts across two opposite edges of the base, it forms a triangle.

So if the slice goes from apex to base edge, it forms a triangular cross-section.

✔ So Triangle is correct if the cut is vertical and through the apex.

But the shading shows a horizontal-looking cut.

Wait — let’s recheck:

In #6, the shaded area is horizontal, but it’s cutting through the pyramid, so it should be a square or rectangle?

No — a horizontal slice of a pyramid (parallel to the base) produces a smaller polygon similar to the base.

For a square pyramid, a horizontal slice → square.

But the answer key says triangle, which is wrong.

⛔ Error in answer key for #6.

✔ Correct answer: Square

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🔷 7) Rectangular prism sliced horizontally

- Shape: Rectangular prism
- Slice: Horizontal cut
- Cross-section: Rectangle
✔ Answer: Rectangle
➡️ This is correct — a horizontal slice of a rectangular prism produces a rectangle (same as the base).

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🔷 8) Triangular prism sliced vertically

- Shape: Triangular prism
- Slice: Vertical cut through the middle
- Cross-section: Rectangle
✔ Answer: Rectangle
➡️ Cutting vertically through the prism (from top to bottom) along the length will pass through two rectangular faces, creating a rectangle.

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🔷 9) Pyramid sliced horizontally

- Shape: Pyramid (likely triangular base?)
- Slice: Horizontal cut
- Cross-section: Square
✘ Wait — if it's a triangular pyramid, a horizontal slice would produce a smaller triangle, not a square.

But the diagram shows a pyramid with a triangular base, and the slice is horizontal.

So the cross-section should be a triangle, not a square.

But the answer key says Square.

⛔ Another possible error.

Wait — look again.

The pyramid has four triangular faces, so it's a tetrahedron (triangular pyramid). A horizontal slice would produce a smaller triangle, not a square.

But the answer key says Square.

✘ This is likely an error in the answer key.

Unless the pyramid has a square base, and the slice is horizontal.

But the diagram shows a triangular base.

So if the base is triangular, horizontal slice = triangle.

But the answer key says square.

🚫 Incorrect answer.

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## ✔ Summary of Corrections:

| Problem | Given Answer | Correct Answer | Reason |
|--------|--------------|----------------|--------|
| 1 | Square | ✔ Square | Vertical slice of cube |
| 2 | Rectangle | ✔ Rectangle | Diagonal slice of prism |
| 3 | Square | ✔ Square (if base is square) | Horizontal slice |
| 4 | Rectangle | ✔ Rectangle | Horizontal slice of triangular prism |
| 5 | Triangle | ✔ Triangle | Vertical slice through apex |
| 6 | Triangle | ✘ Square | Horizontal slice of square pyramid → smaller square |
| 7 | Rectangle | ✔ Rectangle | Horizontal slice of prism |
| 8 | Rectangle | ✔ Rectangle | Vertical slice |
| 9 | Square | ✘ Triangle | Horizontal slice of triangular pyramid → triangle |

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## 🛠️ Final Notes:
- The answer key contains errors in problems #6 and #9.
- For #6: If it's a square pyramid, a horizontal slice gives a square.
- For #9: If it's a triangular pyramid, a horizontal slice gives a triangle.
- The diagrams may be misleading or inconsistent with the answers.

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✔ Corrected Answers:

1. Square
2. Rectangle
3. Square
4. Rectangle
5. Triangle
6. Square (not Triangle)
7. Rectangle
8. Rectangle
9. Triangle (not Square)

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Let me know if you'd like a corrected version of the worksheet or explanations with diagrams!