Geometry: Shapes & Angles,polygons) GL ASSESSMENT QUESTIONS 11 plus exam part -7

3D Shapes: Complete 11+ GL Assessment Guide

STUDY POINTS: Properties of 3D Shapes

Key Concepts to Memorize

1. Basic Terminology

• Face: Flat surface of a 3D shape

• Edge: Where two faces meet (a line)

• Vertex (plural: vertices): Corner point where edges meet

• Net: 2D pattern that can be folded to make a 3D shape

2. Euler's Formula (FOR ALL POLYHEDRA)

F + V = E + 2

• Faces + Vertices = Edges + 2

• Example for cube: 6 faces + 8 vertices = 12 edges + 2 ✓

• Test tip: If they give you 2 of the values, use this formula to find the third

3. Common 3D Shapes Properties

Shape	Faces	Edges	Vertices	Special Features
Cube	6 squares	12	8	All edges equal, all faces squares
Cuboid	6 rectangles	12	8	Opposite faces equal
Triangular Prism	5 (2 triangles, 3 rectangles)	9	6	Constant triangular cross-section
Square-based Pyramid	5 (1 square, 4 triangles)	8	5	Apex above center of base
Triangular-based Pyramid (Tetrahedron)	4 triangles	6	4	All faces equilateral triangles
Cylinder	3 (2 circles, 1 curved)	2 curved edges	0	Circular cross-section
Cone	2 (1 circle, 1 curved)	1 curved edge	1	Circular base, apex above center
Sphere	1 curved surface	0	0	No edges or vertices

4. Prisms vs Pyramids

• PRISMS: Two identical parallel bases, rectangular sides

  • Named by shape of base (triangular prism, hexagonal prism)

  • Number of faces = (number of sides of base) + 2

  • Number of vertices = 2 × (number of vertices of base)

  • Number of edges = 3 × (number of sides of base)

• PYRAMIDS: One base, triangular sides meeting at apex

  • Named by shape of base (square pyramid, triangular pyramid)

  • Number of faces = (number of sides of base) + 1

  • Number of vertices = (number of vertices of base) + 1

  • Number of edges = 2 × (number of sides of base)

5. Nets Recognition

• A net must have enough faces to cover the 3D shape

• Cube: 6 squares in arrangement that folds to cover all faces

• Common cube nets: "T" shape, cross shape, etc.

• IMPORTANT: Not all arrangements of 6 squares make a cube!

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PRACTICE QUESTIONS: 3D Shapes (50 Questions)

Section A: Basic Properties (15 Questions)

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

2. A cuboid has how many edges?
   A) 6 B) 8 C) 12 D) 24

3. How many vertices does a triangular prism have?
   A) 5 B) 6 C) 8 D) 9

4. Which shape has exactly one vertex?
   A) Cube B) Cylinder C) Cone D) Sphere

5. A square-based pyramid has:
   A) 5 faces, 8 edges, 5 vertices
   B) 5 faces, 5 edges, 8 vertices
   C) 8 faces, 5 edges, 5 vertices
   D) 5 faces, 5 edges, 5 vertices

6. True or False: A sphere has faces, edges, and vertices.

7. How many edges meet at each vertex of a cube?
   A) 2 B) 3 C) 4 D) 6

8. Which 3D shape has 2 circular faces and 1 curved surface?
   A) Cone B) Cylinder C) Sphere D) Hemisphere

9. A tetrahedron has how many triangular faces?
   A) 3 B) 4 C) 5 D) 6

10. Euler's formula states:
    A) F + V = E + 2
    B) F + E = V + 2
    C) E + V = F + 2
    D) F = V + E - 2

11. How many rectangular faces does a triangular prism have?
    A) 2 B) 3 C) 4 D) 5

12. Which shape has all faces as triangles?
    A) Cube B) Tetrahedron C) Square pyramid D) Both B and C

13. A hexagonal prism has how many faces?
    A) 6 B) 8 C) 10 D) 12

14. How many edges does a pentagonal pyramid have?
    A) 5 B) 10 C) 15 D) 20

15. Which shape has no flat faces?
    A) Cube B) Sphere C) Cone D) Cylinder

Section B: Using Euler's Formula (10 Questions)

16. A polyhedron has 8 faces and 12 vertices. How many edges does it have?
    A) 16 B) 18 C) 20 D) 22

17. A shape has 6 vertices and 12 edges. How many faces does it have?
    A) 6 B) 7 C) 8 D) 9

18. Using F + V = E + 2, if F = 7 and E = 15, then V = ?
    A) 8 B) 9 C) 10 D) 11

19. A cube satisfies Euler's formula. True or False?

20. Which of these follows Euler's formula?
    A) F=5, V=5, E=8
    B) F=6, V=8, E=12
    C) F=4, V=4, E=6
    D) All of the above

21. A polyhedron has 9 faces and 14 vertices. How many edges?
    A) 19 B) 21 C) 23 D) 25

22. If a shape has F=10 and V=16, then E must be:
    A) 22 B) 24 C) 26 D) 28

23. A triangular prism: F=5, V=6, E=9. Does it satisfy Euler's formula?

24. Which set of numbers cannot represent a polyhedron?
    A) F=4, V=4, E=6
    B) F=6, V=8, E=12
    C) F=5, V=6, E=10
    D) F=7, V=10, E=15

25. A shape has twice as many edges as faces. If it has 8 vertices, how many faces?

Section C: Nets of 3D Shapes (10 Questions)

26. Which net will make a cube?
    [Imagine: Four options showing different arrangements of 6 squares]
    A) T-shape of 6 squares
    B) Straight line of 6 squares
    C) 3×2 rectangle of squares
    D) Cross shape of 6 squares

27. How many different nets of a cube are possible?
    A) 6 B) 8 C) 11 D) 24

28. Which net will make a square-based pyramid?
    [Imagine: Options with square and triangles]

29. True or False: This arrangement of squares will make a cube when folded.

30. The net of a cylinder consists of:
    A) 2 circles and 1 rectangle
    B) 1 circle and 1 rectangle
    C) 2 circles and 2 rectangles
    D) 3 circles

31. When folded, which net makes a tetrahedron?
    [Imagine: 4 equilateral triangles in different arrangements]

32. A cube's net has 6 squares. How many edges will the cube have when folded?

33. Which is NOT a net of a cube?
    [Visual question - typically one with squares arranged so they overlap when folded]

34. The net of a triangular prism contains:
    A) 2 triangles and 3 rectangles
    B) 3 triangles and 2 rectangles
    C) 2 triangles and 4 rectangles
    D) 4 triangles and 2 rectangles

35. True or False: A sphere has a net that can be laid flat.

Section D: Word Problems & Applications (15 Questions)

36. A cube has a volume of 64 cm³. What is the length of one edge?
    A) 2 cm B) 4 cm C) 8 cm D) 16 cm

37. A cuboid measures 5 cm × 4 cm × 3 cm. What is its volume?
    A) 12 cm³ B) 47 cm³ C) 60 cm³ D) 120 cm³

38. The surface area of a cube is 54 cm². What is the area of one face?
    A) 6 cm² B) 9 cm² C) 12 cm² D) 18 cm²

39. How many more vertices does a cube have than a tetrahedron?
    A) 2 B) 4 C) 6 D) 8

40. A square-based pyramid has a base perimeter of 20 cm. What is the length of one base edge?
    A) 4 cm B) 5 cm C) 10 cm D) 20 cm

41. If you cut a cube parallel to one face, what shape is the cross-section?
    A) Triangle B) Square C) Rectangle D) Hexagon

42. A cylinder has radius 7 cm and height 10 cm. Volume = ? (π = 22/7)
    A) 154 cm³ B) 440 cm³ C) 1540 cm³ D) 3080 cm³

43. Which 3D shape would be made by rotating a rectangle about one of its sides?
    A) Sphere B) Cylinder C) Cone D) Cuboid

44. A cube has all edges 6 cm. What is its total surface area?
    A) 36 cm² B) 72 cm² C) 144 cm² D) 216 cm²

45. A triangular prism has a triangular base with sides 3 cm, 4 cm, 5 cm. If the prism is 10 cm long, what is its volume?
    A) 30 cm³ B) 60 cm³ C) 120 cm³ D) 600 cm³

46. How many cubes of side 2 cm can fit into a cuboid of dimensions 10 cm × 8 cm × 6 cm?
    A) 60 B) 120 C) 240 D) 480

47. The net of a 3D shape has 5 faces: 1 square and 4 triangles. What is the shape?
    A) Square pyramid B) Triangular prism C) Cube D) Cuboid

48. A shape has 6 faces, all squares. What is it?
    A) Cube B) Cuboid C) Square pyramid D) Triangular prism

49. True or False: A cone has 2 faces and 1 edge.

50. Which shape has exactly 8 edges?
    A) Cube B) Square pyramid C) Triangular prism D) Tetrahedron

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ADDITIONAL PRACTICE: GL Assessment Style (30 Questions)

51. Look at this net. When folded, which 3D shape does it make?
    [Net with 2 hexagons and 6 rectangles]
    A) Hexagonal prism B) Hexagonal pyramid C) Cube D) Cuboid

52. How many faces does a pentagonal prism have?
    A) 5 B) 6 C) 7 D) 8

53. A shape has 7 faces, 10 vertices. How many edges?
    A) 15 B) 16 C) 17 D) 18

54. Which of these is NOT a polyhedron?
    A) Cube B) Cylinder C) Tetrahedron D) Square pyramid

55. All the faces of a cube are:
    A) Rectangles B) Squares C) Triangles D) Circles

56. How many edges does a triangular-based pyramid have?
    A) 4 B) 6 C) 8 D) 12

57. Point A is a vertex of a cube. How many other vertices are directly connected to A by an edge?
    A) 2 B) 3 C) 4 D) 6

58. Which shape has the same number of faces as a cube?
    A) Tetrahedron B) Square pyramid C) Cuboid D) Triangular prism

59. A cube is cut diagonally from one vertex to the opposite vertex. What shape is the cross-section?
    A) Square B) Rectangle C) Triangle D) Hexagon

60. How many rectangular faces does a square-based pyramid have?
    A) 0 B) 1 C) 4 D) 5

61. Which shape would be formed by rotating a right-angled triangle about one of its perpendicular sides?
    A) Sphere B) Cylinder C) Cone D) Pyramid

62. A polyhedron has 12 edges and 6 faces. How many vertices does it have?
    A) 6 B) 8 C) 10 D) 12

63. True or False: A cylinder has 3 faces and 2 edges.

64. The base of a pyramid is a hexagon. How many triangular faces does it have?
    A) 4 B) 5 C) 6 D) 7

65. Which shape has exactly 5 vertices?
    A) Cube B) Triangular prism C) Square pyramid D) Cuboid

66. If all edges of a cube are doubled, how many times larger is the volume?
    A) 2 times B) 4 times C) 6 times D) 8 times

67. How many edges does an octagonal prism have?
    A) 16 B) 18 C) 24 D) 30

68. Which shape has no vertices?
    A) Cube B) Cone C) Sphere D) Pyramid

69. A tetrahedron has how many edges?
    A) 4 B) 6 C) 8 D) 12

70. The Great Pyramid of Giza is an example of:
    A) Square pyramid B) Triangular prism C) Cube D) Cone

71. How many faces meet at each vertex of a tetrahedron?
    A) 2 B) 3 C) 4 D) 6

72. Which shape has 2 circular faces?
    A) Cone B) Cylinder C) Sphere D) Hemisphere

73. A dice is an example of a:
    A) Cube B) Cuboid C) Pyramid D) Sphere

74. How many more faces does a cube have than a tetrahedron?
    A) 1 B) 2 C) 3 D) 4

75. True or False: All prisms have two identical parallel faces.

76. A shape has F = 8, V = 12. Using Euler's formula, E = ?
    A) 16 B) 18 C) 20 D) 24

77. Which shape has exactly 1 curved face?
    A) Sphere B) Cylinder C) Cone D) Hemisphere

78. How many faces does a rectangular prism have?
    A) 4 B) 6 C) 8 D) 12

79. A triangular pyramid is also called:
    A) Tetrahedron B) Square pyramid C) Prism D) Cube

80. Which shape can have faces that are all different shapes?
    A) Cube B) Cuboid C) Square pyramid D) Triangular prism

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PREVIOUS YEAR QUESTIONS SIMULATION (20 Questions)

81. GL 2022: Which net will make a cube? [Visual question with 4 options]

82. GL 2021: A polyhedron has 6 faces and 8 vertices. How many edges does it have?
    A) 10 B) 12 C) 14 D) 16

83. GL 2020: How many edges does a square-based pyramid have?
    A) 5 B) 6 C) 8 D) 10

84. GL 2019: Which shape has exactly one vertex?
    A) Cube B) Cylinder C) Cone D) Sphere

85. GL 2018: A cube has:
    A) 6 faces, 8 edges, 12 vertices
    B) 6 faces, 12 edges, 8 vertices
    C) 8 faces, 12 edges, 6 vertices
    D) 12 faces, 8 edges, 6 vertices

86. GL 2017: True or False: A cylinder has 3 faces and 2 edges.

87. GL 2016: How many faces does a triangular prism have?
    A) 4 B) 5 C) 6 D) 7

88. GL 2015: Which of these is NOT a polyhedron?
    A) Cube B) Tetrahedron C) Cylinder D) Square pyramid

89. GL 2014: A shape has 9 edges and 5 faces. How many vertices?
    A) 4 B) 6 C) 8 D) 10

90. GL 2013: The net shown folds to make which shape? [Net of square and triangles]

91. GL 2012: How many vertices does a hexagonal prism have?
    A) 8 B) 12 C) 16 D) 18

92. GL 2011: Which shape has all faces as triangles?
    A) Cube B) Tetrahedron C) Cuboid D) Cylinder

93. GL 2010: A cube has volume 125 cm³. Length of one edge?
    A) 5 cm B) 10 cm C) 25 cm D) 125 cm

94. GL 2009: How many edges does a pentagonal pyramid have?
    A) 5 B) 10 C) 15 D) 20

95. GL 2008: True or False: A sphere has faces, edges and vertices.

96. GL 2007: Using F + V = E + 2, if F=7, E=15, then V=?
    A) 8 B) 9 C) 10 D) 11

97. GL 2006: Which shape has 2 circular faces?
    A) Cone B) Cylinder C) Sphere D) Hemisphere

98. GL 2005: A tetrahedron has how many faces?
    A) 3 B) 4 C) 5 D) 6

99. GL 2004: How many more vertices does a cube have than a square-based pyramid?
    A) 1 B) 2 C) 3 D) 4

100. GL 2003: Which net will NOT make a cube? [Visual question]

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COMPREHENSIVE ANSWER KEY & SOLUTIONS

Section A Answers:

1. B) 6 - Cube has 6 square faces

2. C) 12 - Cuboid has 12 edges (like a cube)

3. B) 6 - Triangular prism: 2 triangular bases × 3 vertices each = 6 vertices

4. C) Cone - Cone has 1 vertex (apex)

5. A) 5 faces, 8 edges, 5 vertices - Square base (4) + triangular sides (4) = 8 edges

6. False - Sphere has only 1 curved surface, no edges or vertices

7. B) 3 - At each cube corner, 3 edges meet

8. B) Cylinder - Cylinder has 2 circular ends and curved side

9. B) 4 - Tetrahedron = triangular pyramid = 4 triangular faces

10. A) F + V = E + 2 - Euler's formula

11. B) 3 - Triangular prism has 3 rectangular sides

12. B) Tetrahedron - Tetrahedron has 4 triangular faces

13. B) 8 - Hexagonal prism: 6 rectangular sides + 2 hexagonal bases = 8 faces

14. B) 10 - Pentagonal pyramid: 5 base edges + 5 slant edges = 10 edges

15. B) Sphere - Sphere is perfectly curved, no flat faces

Section B Answers (Euler's Formula):

16. B) 18 - F+V=E+2 → 8+12=E+2 → 20=E+2 → E=18

17. C) 8 - F+6=12+2 → F+6=14 → F=8

18. C) 10 - 7+V=15+2 → 7+V=17 → V=10

19. True - Cube: 6+8=12+2 → 14=14 ✓

20. D) All - Check each: A)5+5=8+2 ✓ B)6+8=12+2 ✓ C)4+4=6+2 ✓

21. B) 21 - 9+14=E+2 → 23=E+2 → E=21

22. B) 24 - 10+16=E+2 → 26=E+2 → E=24

23. Yes - 5+6=9+2 → 11=11 ✓

24. C) F=5, V=6, E=10 - 5+6≠10+2 (11≠12)

25. 6 - Let F=x, then E=2x. x+8=2x+2 → 8=x+2 → x=6

Section C Answers (Nets):

26. D) Cross shape - Classic cube net

27. C) 11 - There are exactly 11 distinct cube nets

28. Square with 4 triangles attached to each side

29. Depends on arrangement - Need visual

30. A) 2 circles and 1 rectangle - Rectangle wraps around to form curved surface

31. 4 equilateral triangles - Various arrangements possible

32. 12 - Cube always has 12 edges regardless of net

33. Any arrangement where squares overlap when folded

34. A) 2 triangles and 3 rectangles

35. False - Sphere cannot be laid flat without distortion

Section D Answers:

36. B) 4 cm - ∛64 = 4

37. C) 60 cm³ - 5×4×3 = 60

38. B) 9 cm² - 54÷6 = 9

39. B) 4 - Cube:8 vertices, Tetrahedron:4 vertices, difference=4

40. B) 5 cm - Square perimeter=20, each side=20÷4=5

41. B) Square - Cutting parallel to face gives same shape as face

42. C) 1540 cm³ - V=πr²h=(22/7)×49×10=1540

43. B) Cylinder - Rotating rectangle about side = cylinder

44. D) 216 cm² - 6×(6×6)=6×36=216

45. B) 60 cm³ - Area of triangle=(3×4)/2=6, Volume=6×10=60

46. A) 60 - Volume of cuboid=480 cm³, small cube=8 cm³, 480÷8=60

47. A) Square pyramid

48. A) Cube

49. True - Cone: 1 circular face, 1 curved face, 1 circular edge

50. B) Square pyramid - 8 edges (4 base + 4 slant)

Additional Practice Answers (51-80):

51. A) Hexagonal prism

52. C) 7 (5 rectangles + 2 pentagons)

53. A) 15 (7+10=E+2 → E=15)

54. B) Cylinder (not a polyhedron - has curved surface)

55. B) Squares

56. B) 6

57. B) 3 (each vertex connects to 3 others)

58. C) Cuboid (also has 6 faces)

59. D) Hexagon

60. A) 0 (all triangular faces)

61. C) Cone

62. B) 8 (F+V=E+2 → 6+V=12+2 → V=8)

63. True

64. C) 6

65. C) Square pyramid

66. D) 8 times (volume scales by cube of scale factor)

67. C) 24 (8×3=24)

68. C) Sphere

69. B) 6

70. A) Square pyramid

71. B) 3

72. B) Cylinder

73. A) Cube

74. B) 2 (cube:6, tetrahedron:4, difference=2)

75. True (definition of prism)

76. B) 18 (8+12=E+2 → E=18)

77. C) Cone

78. B) 6 (rectangular prism = cuboid)

79. A) Tetrahedron

80. B) Cuboid

Previous Year Simulation Answers (81-100):

81. [Visual - usually cross or T shape]

82. B) 12 (6+8=E+2 → E=12)

83. C) 8

84. C) Cone

85. B) 6 faces, 12 edges, 8 vertices

86. True

87. B) 5

88. C) Cylinder

89. B) 6 (5+V=9+2 → V=6)

90. Square-based pyramid

91. B) 12 (hexagon has 6 vertices, prism has 2 bases: 6×2=12)

92. B) Tetrahedron

93. A) 5 cm (∛125=5)

94. B) 10

95. False

96. C) 10 (7+V=15+2 → V=10)

97. B) Cylinder

98. B) 4

99. C) 3 (cube:8, square pyramid:5, difference=3)

100. [Visual - arrangement that overlaps]

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STUDY STRATEGIES & TIPS

Memory Tricks:

1. Cube/Cuboid: Think "6-12-8" (Faces-Edges-Vertices)

2. Square pyramid: Think "5-8-5"

3. Triangular prism: Think "5-9-6"

4. Tetrahedron: Think "4-6-4" (all 4's and 6's)

Visualization Practice:

1. Look at everyday objects and identify their 3D shape properties

2. Practice drawing nets from memory

3. Use clay or building blocks to make shapes and count elements

Exam Technique:

1. For Euler's formula problems: Write down F+V=E+2 immediately

2. For net questions: Mentally fold the net step by step

3. For comparison questions: Write properties of each shape side by side

4. Time management: Easy questions first, mark hard ones to return to

Common Pitfalls to Avoid:

1. Cylinder/cone/sphere are NOT polyhedra (they have curved surfaces)

2. Prisms always have 2 identical parallel bases

3. Pyramids always have triangular sides meeting at apex

4. Cube is a special cuboid with all edges equal

5. Square is a special rectangle with all sides equal

Quick Check Formulas:

1. Prism vertices: 2 × (vertices of base)

2. Prism edges: 3 × (sides of base)

3. Pyramid vertices: (vertices of base) + 1

4. Pyramid edges: 2 × (sides of base)

5. Volume of cube: side³

6. Volume of cuboid: length × width × height

7. Surface area of cube: 6 × side²

Final Advice: Practice identifying shapes from different orientations. Draw them! Count faces, edges, vertices systematically. Use Euler's formula to check your answers. With consistent practice, 3D shape questions become quick marks in the exam.