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3D Shapes and Nets

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3D Shapes and Nets

A small design team is creating display boxes for a travelling exhibition. Use faces, edges, vertices and nets to check whether each package will fold into the intended 3D shape. A net is a flat arrangement of faces that can be folded to make a solid.

Identify the solids

Use the shape guide, then solve the team’s first checks.

Triangular prism

Square-based pyramid

Hexagonal prism

1.The triangular-prism display case is a right triangular prism and is made from flat faces. Which set of faces does it have?

2 triangles and 3 rectangles
3 triangles and 2 rectangles
2 rectangles and 3 hexagons
6 triangles

2.A cube is used as a small sample box. How many faces, edges and vertices does it have altogether? Give the three numbers in that order.

3.Which solid in the guide has exactly four triangular faces and one square face?

4.A box has 6 rectangular faces, 12 edges and 8 vertices. Name the most general 3D shape it could be. Could it also be a cube? Explain briefly.

Test the nets

Check both the number and arrangement of faces. A correct collection of faces does not always make a foldable net.

Net A □ □□□□ □

Net B □□□□□□

5.Which proposed arrangement, Net A or Net B, can fold into a cube? Explain what happens when you fold the other arrangement.

6.A net for a right triangular prism must contain two triangles and three rectangles. True or false? Give one reason.

TrueFalse

7.Complete the net checklist for a hexagonal prism: it needs hexagons and rectangles. How many faces does the completed prism have?

Design the package

Choose faces carefully and show how they connect.

8.Design a net for a square-based pyramid in the box above. Draw one square with four triangles attached, one on each side of the square. Label the faces and state how many faces, edges and vertices the folded solid has.

9.A designer wants a gift box shaped like a right triangular prism. Describe the faces needed for its net and explain how the rectangles and triangles meet when folded.