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3D Shapes and Nets
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3D Shapes and Nets
A local food stall wants a new cardboard package. Use your knowledge of 3D shapes and nets to help choose and plan a practical design. Show working where needed.
Shape detectives
Use face, edge and vertex properties to identify and compare solids.
1.A triangular prism is being considered for a package. How many faces, edges and vertices does it have?
2.A sealed package has 6 rectangular faces, 12 edges and 8 vertices. Which solid is it most likely to be?
- A rectangular prism
- A triangular prism
- A square-based pyramid
- A cylinder
3.A square-based pyramid has a square base and four triangular sides. Complete its properties: faces, edges and vertices.
4.Which statement correctly distinguishes a cone from a pyramid?
- A cone has a curved surface and a circular base; a pyramid has flat polygonal faces.
- A cone has vertices; a pyramid has none.
- Both have only curved surfaces.
- A cone has a rectangular base; a pyramid has a circular base.
Nets that work
A net is a flat arrangement of faces that can fold to form a 3D solid.
5.Three candidate nets are described below. Net A is made of six squares: four squares in a row, with one square attached above the second square and one attached below the third square. Net B is made of three rectangles in a row, with a triangle attached above and below the middle rectangle. Net C is made of six squares in a straight row. Which net can fold to make a cube? Explain why one of the other arrangements will not make a cube.
6.Using the candidate nets described in the previous question, which net makes a triangular prism, and what shapes are its faces?
7.True or false: every arrangement of six squares is a net for a cube. Give one reason for your answer.
TrueFalse
Plan the package
Put your geometry knowledge to work on a practical design.
8.A snack box is a closed rectangular prism measuring 12 cm long, 8 cm wide and 5 cm high. Calculate the total area of cardboard needed, ignoring tabs and waste. Show your calculation.
9.The stall wants the box to hold 480 cm³ of snacks. The base is 12 cm by 8 cm. What height should the box be? Include the volume relationship you use.
10.You are asked to sketch a net for the 12 cm × 8 cm × 5 cm snack box. Name the six rectangles your net must contain, then draw a possible arrangement.
3 printable pages
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