Multiple Nets of 3D Shapes worksheet for identifying correct 2D nets for various 3D geometric figures.

Of course! Let’s solve each question step by step. The task is to choose the different net — meaning, identify which option cannot be folded into the given 3D shape.

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1. Choose the different nets of a cone.

A cone has:
- One circular base.
- One curved lateral surface that forms a sector of a circle when flattened.

✔ Correct nets for a cone must show:
- A circle (the base).
- A sector (the curved surface).

Let’s look at the options:

- a) Circle + sector → ✔ Valid net.
- b) Circle + sector → ✔ Valid net.
- c) Two separate shapes: a triangle and a circle → ✘ Triangle is not part of a cone’s net. A cone’s lateral surface is curved, not flat triangular.
- d) Circle + sector → ✔ Valid net.

➡️ Answer: c) — It’s the only one with a triangle, which doesn’t belong in a cone’s net.

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2. Select the different nets of a triangular prism.

A triangular prism has:
- Two triangular bases.
- Three rectangular lateral faces.

✔ Valid nets will have:
- Two triangles (same size, usually on opposite ends).
- Three rectangles connecting them.

Look at the options:

- a) Two triangles on top and bottom, three rectangles in between → ✔ Valid.
- b) Two triangles on the sides, three rectangles → ✔ Valid.
- c) Two triangles on the same side, three rectangles → ✔ Can still fold into a prism.
- d) Two triangles on the same side, but arranged so they are adjacent — this would cause overlap or misalignment when folding. More importantly, the rectangles are not positioned to connect both triangles properly. This net cannot form a closed triangular prism without gaps or overlaps.

➡️ Answer: d) — The arrangement makes it impossible to fold into a proper triangular prism.

*(Note: Some might argue b or c, but d is clearly flawed because the two triangles are not separated by the three rectangles needed to form the sides.)*

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3. Pick the different nets of a cylinder.

A cylinder has:
- Two circular bases.
- One rectangular lateral surface (when unrolled).

✔ Valid nets show:
- Two circles.
- One rectangle connecting them (or placed next to them).

Options:

- a) Two circles side-by-side, rectangle above → ✔ Can fold into cylinder.
- b) Two circles on top/bottom of rectangle → ✔ Classic net.
- c) Two circles on left/right of rectangle → ✔ Also valid.
- d) Two circles and a rectangle, but the rectangle is too small or misaligned? Actually, looking closely — this net has two circles and a rectangle, but the rectangle is NOT connected to the circles in a way that allows folding. Wait — actually, all four seem plausible? Let’s think again.

Actually, option d) shows two circles and a rectangle, but the rectangle is not attached to either circle — it’s just floating nearby. In a proper net, the rectangle must be attached to at least one circle (usually both) to allow folding into a 3D shape.

In contrast, a, b, c all show the rectangle connected to the circles.

➡️ Answer: d) — The rectangle is not connected to the circles, so it’s not a valid net.

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4. Choose the different nets of a square pyramid.

A square pyramid has:
- One square base.
- Four triangular lateral faces.

✔ Valid nets will have:
- One square.
- Four triangles attached to its sides.

Options:

- a) Square in center, four triangles around → ✔ Classic net.
- b) Square with triangles on two opposite sides → ✔ Can still fold into pyramid.
- c) Two triangles on top, two on bottom — looks like a diamond shape → ✔ Still can fold.
- d) This one shows a square with triangles attached, but one triangle is missing — wait, no, it has four triangles? Actually, looking closely — it has five triangles! That’s the problem.

Wait — let’s count:

- a) 4 triangles → ✔
- b) 4 triangles → ✔
- c) 4 triangles → ✔
- d) Has five triangles — one extra! A square pyramid only needs 4 triangular faces.

➡️ Answer: d) — It has 5 triangles instead of 4 — incorrect number of faces.

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5. Pick the different nets of a cube.

A cube has 6 square faces.

✔ Valid nets must have 6 squares arranged so they can fold into a cube without overlapping or gaps.

Common invalid nets include those with more than 4 squares in a row, or “T” shapes that don’t close properly.

Options:

- a) Looks like a “T” shape — 3 in a row, with one on top and two on bottom? Actually, it’s 3 vertical, with one on left and right — this is a valid net (like a cross missing one arm). Wait — let’s check standard cube nets.

Actually, let’s analyze:

- a) 6 squares: 3 in a column, one sticking out left from middle, one right from middle, one below bottom → ✔ Valid.
- b) 4 in a row, one above second, one below third → ✔ Standard “zigzag” net — valid.
- c) Cross shape — 4 in a row, one above center, one below center → ✔ Classic valid net.
- d) 3 in a row, then 2 stacked on the right end, and one hanging off the bottom — this is invalid. If you try to fold it, two faces will overlap or leave a gap. Specifically, the “staircase” shape with 3+2+1 doesn’t form a closed cube.

➡️ Answer: d) — This arrangement cannot fold into a cube without overlap or gaps.

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## ✔ Final Answers:

1. c
2. d
3. d
4. d
5. d

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## 📝 Summary:

| Question | Correct Answer | Reason |
|----------|----------------|--------|
| 1. Cone | c | Has a triangle, not a sector. |
| 2. Triangular Prism | d | Triangles not properly connected by rectangles. |
| 3. Cylinder | d | Rectangle not attached to circles. |
| 4. Square Pyramid | d | Has 5 triangles instead of 4. |
| 5. Cube | d | Net cannot fold into a cube without overlap/gap. |

Let me know if you’d like diagrams or folding animations explained!