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3D Shape Properties

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3D Shape Properties

Sione is planning a small pop-up kiosk for a weekend market in Aotearoa New Zealand. Use your knowledge of faces, edges, vertices, nets and 3D objects to check her designs. For this worksheet, count only flat faces when a question says “flat faces”; curved surfaces are not flat faces.

Inspect the solids

Use the descriptions below to answer the questions.

1.The storage box is a cuboid. How many faces, edges and vertices does it have? Give your answer in that order.

2.The drink can is a cylinder. Which description is correct when counting flat faces?

It has 3 flat faces, 2 edges and 0 vertices.
It has 2 flat faces, 2 circular edges and 0 vertices.
It has 2 flat faces, 1 edge and 1 vertex.
It has 1 flat face, 0 edges and 2 vertices.

3.Sione says, “A sphere has one curved surface and no flat faces, edges or vertices.” Is her statement true or false? Explain what makes the sphere different from the other kiosk shapes.

4.Write the correct solid beside each clue: cube, cone, triangular prism or square-based pyramid.

A. Two triangular faces and three rectangular faces
B. Six equal square faces
C. One circular base, one curved surface and one vertex
D. One square base and four triangular faces meeting at one vertex

Cube
Square-based pyramid
Cone
Triangular prism

Nets for the kiosk

A net is a flat pattern that can be folded to make a 3D solid.

5.Which proposed net can fold to make a cube? Choose the best answer and explain why the other patterns will not work.

Six equal squares in a straight row
Six equal squares arranged as four in a row, with one square attached above the second and one below the second
Five equal squares arranged in a cross
Six equal squares arranged as a 2-by-3 rectangle

6.A triangular pyramid has four triangular faces. Describe how to arrange four triangles to make a net that can fold into the pyramid.

7.In a sentence or two, explain how a flat net becomes a 3D shape. Include what happens to the edges where faces meet.

Apply your geometry

Use properties and simple models to make good design choices.

8.For each kiosk item, name a 3D solid it most closely resembles: a dice, a drink can and an ice-cream cone.

9.A cube-shaped gift box and a cuboid-shaped storage box have the same number of faces, edges and vertices. What property makes the cube a special type of cuboid?

10.For a convex polyhedron, faces (F), vertices (V) and edges (E) satisfy F + V − E = 2. Check the relationship for a triangular prism with 5 faces, 6 vertices and 9 edges. Show the calculation.

11.Sketch the front view and the top view of a cuboid-shaped kiosk box. Assume its front is a rectangle and look straight down for the top view.