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About 3D Shapes & Nets — Class 6 IB

Identify prisms, pyramids, and cylinders; draw and interpret nets of 3D shapes. This topic is part of the IB Class 6 mathematics syllabus (chapter: Unit 13). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

3D Shapes & Nets — solved examples for Class 6 IB

Example 1easy

How many faces does a cube have?
  1. A)4
  2. B)6
  3. C)8
  4. D)12

Step-by-step solution

  1. A cube has 6 faces
  2. Top, bottom, front, back, left, and right

Answer: 6

Example 2medium

Euler's formula states that for any polyhedron: VE+F=2V - E + F = 2. A cuboid has 8 vertices and 12 edges. How many faces does it have?
  1. A)4
  2. B)5
  3. C)6
  4. D)8

Step-by-step solution

  1. Euler's formula: V − E + F = 2
  2. 8 − 12 + F = 2
  3. −4 + F = 2
  4. F = 6

Answer: 6

Example 3hard

A polyhedron has 20 triangular faces. Using Euler's formula, if it has 12 vertices, how many edges does it have?
  1. A)20
  2. B)25
  3. C)30
  4. D)35

Step-by-step solution

  1. V − E + F = 2
  2. 12 − E + 20 = 2
  3. 32 − E = 2
  4. E = 30
  5. This is actually an icosahedron (12 vertices, 30 edges, 20 faces)

Answer: 30

Practice questions on 3D Shapes & Nets

  1. Q1.easy

    How many edges does a cube have?
    1. A)6
    2. B)8
    3. C)10
    4. D)12
    Show answer

    Answer: 12

    Hint: Count the lines where two faces meet.

  2. Q2.easy

    How many vertices does a cube have?
    1. A)4
    2. B)6
    3. C)8
    4. D)12
    Show answer

    Answer: 8

    Hint: Vertices are the corners — count them on top and bottom.

  3. Q3.easy

    What 3D shape has a circular base and one curved surface that comes to a point?
    1. A)Cylinder
    2. B)Cone
    3. C)Sphere
    4. D)Pyramid
    Show answer

    Answer: Cone

    Hint: Think of an ice cream cone.

  4. Q4.medium

    A hexagonal prism has a regular hexagon as its base. How many faces does it have?
    1. A)6
    2. B)7
    3. C)8
    4. D)12
    Show answer

    Answer: 8

    Hint: A prism has 2 bases plus one rectangular face for each side of the base.

  5. Q5.medium

    Which of these arrangements of 6 squares does NOT fold into a cube?
    1. A)A cross shape (t-shape with extra)
    2. B)A straight line of 6 squares
    3. C)An L-shape of 4 with 2 on the side
    4. D)A T-shape with 2 extras
    Show answer

    Answer: A straight line of 6 squares

    Hint: If you try to fold a straight line of 6 squares, two faces would overlap.

  6. Q6.medium

    A pentagonal prism has how many edges?
    1. A)10
    2. B)12
    3. C)15
    4. D)20
    Show answer

    Answer: 15

    Hint: For a prism with an n-sided base, the number of edges is 3n.

  7. Q7.hard

    A solid has faces that are all equilateral triangles and has 4 faces. What is this shape called?
    1. A)Triangular prism
    2. B)Tetrahedron
    3. C)Octahedron
    4. D)Square pyramid
    Show answer

    Answer: Tetrahedron

    Hint: It's a pyramid made entirely of triangles — even the base is a triangle.

  8. Q8.hard

    The surface area of a cube with edge length 5 cm is:
    1. A)25 cm225 \text{ cm}^2
    2. B)125 cm2125 \text{ cm}^2
    3. C)150 cm2150 \text{ cm}^2
    4. D)750 cm2750 \text{ cm}^2
    Show answer

    Answer: 150 cm2150 \text{ cm}^2

    Hint: Surface area of a cube = 6×(edge)26 \times (\text{edge})^2

  9. Q9.hard

    A cuboid has dimensions 8 cm × 5 cm × 3 cm. What is its surface area?
    1. A)120 cm2120 \text{ cm}^2
    2. B)158 cm2158 \text{ cm}^2
    3. C)240 cm2240 \text{ cm}^2
    4. D)316 cm2316 \text{ cm}^2
    Show answer

    Answer: 158 cm2158 \text{ cm}^2

    Hint: Surface area = 2(lb + bh + lh) where l, b, h are the dimensions.

These are 9 of the 60 questions available for 3D Shapes & Nets. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.