Identify the 2D shape formed by slicing each 3D shape in the worksheet.

Let’s go through each problem one by one. We’re looking at 3D shapes and imagining what flat 2D shape you’d get if you sliced them with a plane (like cutting with a knife). The slice is shown as a shaded area in each diagram.

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Problem 1:
The 3D shape is a pyramid with a square base. The slice goes straight down from the top point to the middle of the base — it cuts through two opposite sides of the base and the apex. That makes a triangle.

→ Answer: b) triangle

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Problem 2:
This is a cube. The slice is horizontal, going straight across the middle — parallel to the top and bottom faces. Since all faces of a cube are squares, but when you cut horizontally through the middle, you get a rectangle? Wait — actually, no! A cube has equal length, width, and height. If you slice it horizontally through the center, you get a square… but wait — look again.

Actually, in the drawing, the slice is not aligned with the face — it looks like it’s slicing diagonally through four vertical edges? No — let me recheck.

Wait — looking carefully: the slice is horizontal, cutting through the middle of the cube, parallel to the top and bottom. In a cube, that would give a square. But option “square” isn’t listed for #2! Options are: a) rectangle, b) ellipse, c) circle.

Hmm — maybe the drawing is misleading? Or perhaps it’s not a perfect cube? Actually, in many textbooks, even if it’s a cube, they might show a rectangular cross-section if the view is perspective. But logically, a horizontal slice through a cube should be a square.

But since “square” isn’t an option, and “rectangle” is — and a square is a type of rectangle — maybe they want “rectangle”.

Wait — let’s look at the image again mentally: the slice is drawn as a parallelogram? No — in standard problems, if you slice a cube horizontally, you get a square. But perhaps in this case, because of how it’s drawn, it’s meant to be a rectangle? Or maybe it’s not a cube but a rectangular prism?

Looking back: the shape is labeled as a cube? Actually, in the image, it’s drawn as a cube, but sometimes in diagrams, they use “cube” loosely. However, given the options, and since a square is a special rectangle, and “square” isn’t an option, the best answer is a) rectangle.

But wait — let me double-check problem 6 — there’s a cylinder being sliced vertically, which gives a rectangle. So for consistency...

Actually, I think I made a mistake. Let me reevaluate Problem 2.

In Problem 2, the 3D shape is a cube, and the slice is horizontal — cutting through the middle, parallel to the bases. In a cube, that cross-section is a square. But since “square” is not an option, and “rectangle” is, and a square is a rectangle, we can choose “rectangle”. But that feels off.

Wait — perhaps the slice is not horizontal? Looking at the diagram description: it says “the slice is shown as a shaded area”. In many such worksheets, for a cube, if you slice it horizontally, it’s a square. But maybe in this case, the slice is diagonal? No — the description says “horizontal”.

Alternatively, perhaps the shape is not a cube but a rectangular prism? The problem doesn’t specify, but the drawing might imply it’s a cube.

Given the options, and since “square” isn’t available, and “rectangle” is the closest, I’ll go with a) rectangle — but I’m uneasy.

Wait — let’s skip and come back.

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Problem 3:
Shape is a pentagonal prism (5-sided base). The slice is horizontal, cutting through the middle, parallel to the bases. So the cross-section should be the same as the base — a pentagon.

Options: a) pentagon, b) square, c) ellipse → so a) pentagon

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Problem 4:
Shape is a sphere. Any slice through a sphere is a circle (as long as it’s not tangent or missing the sphere). Here, the slice goes through the center, so definitely a circle.

Options: a) triangle, b) hexagon, c) circle → c) circle

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Problem 5:
Shape is a triangular prism (base is a triangle). The slice is vertical, cutting through the three rectangular faces — it’s parallel to the triangular bases? No — looking at the diagram: the slice is cutting through the prism in a way that it intersects all three rectangular faces, and the resulting shape is a triangle? Or is it?

Actually, if you slice a triangular prism vertically, perpendicular to the bases, you get a rectangle. But here, the slice seems to be at an angle? Or is it parallel to the triangular faces?

Wait — the shaded area is a triangle. And the slice is cutting through the prism such that it hits the three lateral faces, forming a triangle. Yes — if you slice a triangular prism with a plane that is not parallel to the bases but cuts through all three rectangular faces, you can get a triangle.

Actually, standard result: if you slice a triangular prism with a plane parallel to the triangular bases, you get a triangle. But in this diagram, the slice appears to be vertical and cutting across the length — which would give a rectangle.

I need to visualize better.

Upon second thought: in many textbook diagrams, for a triangular prism, if you make a vertical slice that is parallel to the triangular ends, you get a rectangle. But if you slice it diagonally, you might get a triangle.

Looking at the options: a) ellipse, b) pentagon, c) triangle

And the shaded region is drawn as a triangle. So likely, the slice is intended to produce a triangle. How? If the slice is parallel to the triangular bases, then yes — cross-section is a triangle.

Yes — that must be it. So c) triangle

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Problem 6:
Shape is a cylinder. The slice is vertical, cutting straight down through the center — so it’s a rectangle (height of cylinder by diameter of base).

Options: a) rectangle, b) circle, c) square → a) rectangle

Now back to Problem 2.

Problem 2: Cube, horizontal slice. Should be square. But options are rectangle, ellipse, circle. Since square is a rectangle, and it’s the only plausible choice, we pick a) rectangle.

Perhaps in some contexts, they consider the cross-section of a cube as a rectangle when viewed in perspective, but mathematically it’s a square. Given the options, “rectangle” is acceptable.

So final answers:

1) b) triangle
2) a) rectangle
3) a) pentagon
4) c) circle
5) c) triangle
6) a) rectangle

Let me verify once more.

For Problem 5: Triangular prism, slice parallel to bases → triangle. Yes.

For Problem 2: Even though it's a cube, and cross-section is square, since "square" isn't an option, and "rectangle" includes squares, it's fine.

Okay, confident now.

Final Answer:
1) b
2) a
3) a
4) c
5) c
6) a