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Grade 9 · Geometry of 3D Objects
Geometry of 3-D Objects: Faces, Vertices, Edges & Nets
MEMORANDUM
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  / 14

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

  1. 1
    How many faces, vertices and edges does a cube have?
    (3)
    hidden edges are dashed
    6 faces, 8 vertices, 12 edges✓✓✓ (3)
  2. 2
    State Euler's formula.
    (1)
    F + V − E = 2✓ (1)
  3. 3
    A solid has 5 faces and 6 vertices. How many edges?
    (2)
    a triangular prism
    5 + 6 − E = 2 → E = 9✓✓ (2)
  4. 4
    How many Platonic solids are there?
    (1)
    Five✓ (1)
  5. 5
    How many faces does an octahedron have, and what shape are they?
    (2)
    8 triangular faces✓✓ (2)
  6. 6
    Check Euler's formula for a tetrahedron (4 faces, 4 vertices, 6 edges).
    (2)
    a tetrahedron — 4 triangular faces
    F + V − E = 4 + 4 − 6 ✓ = 2, so Euler's formula holds ✓(2)
  7. 7
    How many edges and vertices does a sphere have?
    (1)
    no edges, no vertices
    None — a sphere has one curved surface only.✓ (1)
  8. 8
    How many squares are in the net of a cube?
    (1)
    6, one for each face✓ (1)
  9. 9
    A net has 2 circles and 1 rectangle. Which solid is it?
    (1)
    A cylinder✓ (1)
TOTAL: 14 marks
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