Interactive worksheet for identifying 2D cross-sections of 3D shapes.

Let’s go through each problem one by one. We’re looking at 3D shapes being sliced (cut) by a flat plane, and we need to figure out what 2D shape appears on the cut surface — that’s called the cross section.

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Problem 1:
The shape is a cone. The slice goes straight down from the tip to the base, cutting it in half vertically.
→ When you slice a cone this way, you get a triangle.
✔ Answer: b) triangle

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Problem 2:
This is a rectangular prism (like a box). The slice cuts horizontally through the middle, parallel to the top and bottom faces.
→ Since the top and bottom are rectangles, slicing parallel to them gives another rectangle.
✔ Answer: a) rectangle

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Problem 3:
This is a pentagonal prism (has a pentagon as its base). The slice cuts straight across, perpendicular to the sides, going through the middle.
→ If you cut straight across a prism like this, you get the same shape as the base — which is a pentagon.
✔ Answer: a) pentagon

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Problem 4:
This is a sphere (ball). Any flat slice through a sphere will always make a circle — no matter how you cut it.
→ Even if it’s not through the center, it’s still a circle (just smaller).
✔ Answer: c) circle

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Problem 5:
This is a triangular prism (base is a triangle). The slice cuts diagonally across two of the rectangular faces.
→ Looking at the angle, it’s cutting through three faces — so the cross section should be a triangle.
Wait — let’s double-check. Actually, when you slice a triangular prism diagonally like this, depending on the angle, you can get different shapes. But here, since it’s cutting through all three rectangular sides and connecting edges, it forms a triangle.
Actually — hold on! Let me think again. In many standard problems, if you slice a triangular prism diagonally from one edge to another non-adjacent edge, you might get a quadrilateral... but looking at the diagram, the slice seems to connect three points — forming a triangle.
But wait — actually, in most textbook examples, this kind of diagonal slice through a triangular prism produces a triangle only if it’s parallel to the base. Here, it’s slanted. Hmm.

Let me reconsider: The slice shown passes through three faces — entering one rectangular face, exiting another, and touching the third? Actually, looking carefully — it enters one side, exits the opposite side, and cuts through the top or bottom? No — in the image, it looks like it’s cutting through three edges — making a triangle.

Actually, I recall now: if you slice a triangular prism with a plane that intersects all three rectangular faces, you get a triangle. Yes — because each intersection with a face is a line segment, and three segments form a triangle.

✔ So answer is: c) triangle

Wait — but option b is pentagon? That doesn’t make sense. Option c is triangle — yes.

Hold on — let me check online logic quickly in my mind: Standard result — slicing a triangular prism diagonally across three faces → triangle. Correct.

✔ Final for #5: c) triangle

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Problem 6:
This is a cylinder. The slice is vertical — going straight up and down, cutting through the curved side and both circular bases.
→ When you slice a cylinder vertically (parallel to its height), you get a rectangle. Why? Because the side is curved, but the cut is flat — so you see the height and the diameter — forming a rectangle.
✔ Answer: a) rectangle

Wait — unless it’s cut exactly through the center? Still a rectangle. Even if off-center, it’s still a rectangle — just narrower. Only if you cut horizontally do you get a circle.

Yes — vertical slice = rectangle.

✔ Answer: a) rectangle

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Now let’s list all answers clearly:

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

I’ve double-checked each one based on standard geometry rules for cross sections.

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