Lesson 1.1: 2D and 3D Shapes: Sides, Vertices, Faces, and Edges
Distinguish 2D polygons from 3D solids by analyzing sides, vertices, flat faces, curved surfaces, and edges.
⏱️ Reading Time: 15 mins
• ❓ 50 Interactive Practice Questions
🌟
Real-Life Story: Shapes and Geometry
Leo is building an obstacle course model on his desk. He selects flat rectangular wooden tiles for ramps and solid cylindrical cans for bridge pillars. By understanding geometric properties, he ensures the structures balance stably.
💡 Core Mathematical Concepts: 2D and 3D Shapes
Focus areas: Circles, triangles, quadrilaterals, cubes, cuboids, cylinders, spheres, cones.
| Concept / Term | Mathematical Definition | Everyday Example |
|---|---|---|
| 2D Plane Shapes | Flat figures with only length and width (circles, triangles, squares, rectangles) | A square sticky note, circular coaster |
| 3D Solid Shapes | Three-dimensional objects with length, width, and height (cubes, cuboids, cylinders, cones, spheres) | A toy dice, cereal carton, soccer ball |
| Faces, Edges & Vertices | A face is a flat surface; an edge is where 2 faces meet; a vertex is a corner point where edges meet | A cube has 6 flat faces, 12 straight edges, and 8 vertices |
| Curved Surfaces | Smooth non-flat boundaries found on spheres, cones, and cylinders | A cylinder has 2 flat circular faces and 1 curved surface |
🔍 Practical Classroom & Everyday Examples
Example 1: Comparing Square vs. Rectangle
A square is a special rectangle with 4 equal sides. A general rectangle has opposite sides equal.
Example 2: Cube vs. Cuboid
Every face of a cube is a square. A cuboid has rectangular faces (at least 4). Both have 6 faces, 12 edges, 8 vertices.
⚠️ Watch Out! Common Mistakes to Avoid
Common Error: Calling a sphere a 2D circle
Correction: A circle is flat on paper (2D). A sphere is a 3D solid that takes up space in the real world.
Common Error: Counting edges on a cylinder as 0
Correction: A cylinder has 2 circular edges where the flat faces meet the curved surface.
🎯 Quick Self-Check Challenge
If you stack 3 identical cubes on top of each other, how many flat square faces are visible from the outside?
Answer & Explanation:
3 separate cubes have 18 total faces. Stacking them hides 4 contact faces (2 pairs of touching faces). Thus, 18 - 4 = 14 external faces remain visible.
🎯 Key Learning Takeaways
Master Shapes and Geometry fundamentals.
📄 Printable Worksheets (5 Available)
Download ready-to-print PDFs for offline student practice with separate parent/teacher answer keys.
G3-M-CH01-WS05
A4 • 15 Qs
Shapes and Geometry — Worksheet 5
2D Shapes, 3D Solids & Perspectives (Sculpture & Ceramic Guild)
G3-M-CH01-WS04
A4 • 15 Qs
Shapes and Geometry — Worksheet 4
2D Shapes, 3D Solids & Perspectives (Robotics Assembly Lab)
G3-M-CH01-WS03
A4 • 15 Qs
Shapes and Geometry — Worksheet 3
2D Shapes, 3D Solids & Perspectives (Packaging Design Factory)
G3-M-CH01-WS02
A4 • 15 Qs
Shapes and Geometry — Worksheet 2
2D Shapes, 3D Solids & Perspectives (Playground Equipment Workshop)
G3-M-CH01-WS01
A4 • 15 Qs
Shapes and Geometry — Worksheet 1
2D Shapes, 3D Solids & Perspectives (Architecture Model Studio)
✍️ Lesson Practice Questions (50 Questions)
Solve these real-world challenges online, test your understanding, and reveal instant step-by-step explanations.
1
Short Answer
Hard
2 Marks
A packaging designer lines all 12 edges of a cube with reflective tape. If each edge is 15 cm long, what is the total length of reflective tape required?
A
180 cm
B
150 cm
C
160 cm
D
200 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
180 cm
Step-by-Step Explanation:
12 edges × 15 cm = 180 cm.
2
Short Answer
Hard
2 Marks
An architect builds a tower by gluing 6 cubes in a vertical stack. If each cube has 6 faces, and adjacent cubes share 1 glued face each, how many exposed outer faces does the tower have?
A
26 faces
B
30 faces
C
30 faces
D
36 faces
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
26 faces
Step-by-Step Explanation:
Each glue joint hides 2 faces. For 6 cubes, there are 5 joints hiding 10 faces: 36 - 10 = 26 exposed faces.
3
Short Answer
Hard
2 Marks
If you slice a standard solid cuboid with a single straight flat cut parallel to its base, what 2D cross-section shape is revealed?
A
A rectangle (or square)
B
A circle
C
A triangle
D
A hexagon
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
A rectangle (or square)
Step-by-Step Explanation:
Cutting parallel to the rectangular base produces a matching rectangular cross-section.
4
Short Answer
Hard
2 Marks
Why can cubes and cuboids be stacked tightly into high storage walls without gaps, while spheres leave empty space?
A
Cubes and cuboids have flat, rectangular faces that tessellate without gaps, whereas spheres only touch at single curved points
B
Spheres are too heavy to stack
C
Cubes have more mass than spheres
D
Spheres only stack when square
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Cubes and cuboids have flat, rectangular faces that tessellate without gaps, whereas spheres only touch at single curved points
Step-by-Step Explanation:
Flat parallel surfaces touch completely and distribute weight evenly, allowing gap-free tessellation in 3D.
5
Short Answer
Medium
1 Mark
Liam looks at an upright traffic cone from directly above and says: 'The top view is a triangle.' Why is Liam incorrect?
A
From directly above, a cone appears as a circle with a center point (apex), not a triangle
B
A cone appears as a square from above
C
A cone has no top view
D
Liam is right; cones always look like triangles
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
From directly above, a cone appears as a circle with a center point (apex), not a triangle
Step-by-Step Explanation:
A cone appears triangular from the front/side, but circular from directly above.
6
Short Answer
Medium
1 Mark
A student claims: 'A rectangle is always a square because both have 4 right angles.' What is the conceptual error in this statement?
A
All squares are rectangles, but not all rectangles are squares because a rectangle's adjacent sides can have different lengths
B
Rectangles have only 3 right angles
C
Squares do not have right angles
D
A rectangle has 5 sides
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
All squares are rectangles, but not all rectangles are squares because a rectangle's adjacent sides can have different lengths
Step-by-Step Explanation:
A square requires all 4 sides to be equal, which is not required for all rectangles.
7
Fill in the Blanks
Medium
1 Mark
Complete the geometry equation: [ ? ] Cubes + 1 Cylinder = 74 edges in total. How many cubes are there?
A
6 cubes
B
7 cubes
C
5 cubes
D
2 cubes
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 cubes
Step-by-Step Explanation:
A cylinder has 2 edges. Total - 2 = 72. Each cube has 12 edges, so 72 ÷ 12 = 6 cubes.
8
Fill in the Blanks
Medium
1 Mark
Identify the mystery solid: 'I have 0 flat faces, 0 straight edges, and 1 continuous curved surface. I can roll smoothly in any direction.'
A
Sphere
B
Cylinder
C
Cone
D
Cube
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Sphere
Step-by-Step Explanation:
A sphere has no flat faces, no straight edges, and can roll in any direction.
9
Short Answer
Medium
1 Mark
In a toy set, children assemble 3 cylindrical towers and 6 cubic blocks. How many circular flat faces are there in total on the towers?
A
6 circular faces
B
8 circular faces
C
3 circular faces
D
12 circular faces
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 circular faces
Step-by-Step Explanation:
Each cylinder has 2 circular faces: 3 × 2 = 6 circular faces.
10
Short Answer
Medium
1 Mark
A stage designer paints all exterior sides of 4 rectangular display boxes (cuboids). If each box has 6 flat faces, how many faces are painted across all 4 boxes?
A
24 faces
B
21 faces
C
28 faces
D
20 faces
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
24 faces
Step-by-Step Explanation:
4 × 6 faces = 24 faces.
11
Short Answer
Medium
1 Mark
At the Sculpture & Ceramic Guild, an artisan glues 6 wooden cubes together in a straight row. How many total flat square faces were on the cubes before gluing?
A
36 flat faces
B
34 flat faces
C
40 flat faces
D
24 flat faces
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
36 flat faces
Step-by-Step Explanation:
Each cube has 6 flat faces. 6 × 6 = 36 flat faces.
12
Multiple Choice
Easy
1 Mark
What 2D shape does a soup can (cylinder) appear to be when viewed directly from the side at eye level?
A
Rectangle
B
Circle
C
Triangle
D
Oval
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Rectangle
Step-by-Step Explanation:
At exact eye level from the side, a cylinder's outline forms a rectangle.
13
Multiple Choice
Easy
1 Mark
How many flat faces and curved surfaces does an upright solid cylinder possess?
A
2 flat circular faces and 1 curved surface
B
1 flat face and 2 curved surfaces
C
3 flat faces and 0 curved surfaces
D
0 flat faces and 1 curved surface
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
2 flat circular faces and 1 curved surface
Step-by-Step Explanation:
A cylinder has 2 flat circular ends and 1 curved surface connecting them.
14
Multiple Choice
Easy
1 Mark
Which 2D shape has exactly 3 straight sides and 3 sharp corners (vertices)?
A
Triangle
B
Rectangle
C
Pentagon
D
Circle
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Triangle
Step-by-Step Explanation:
A triangle is a 3-sided polygon with 3 vertices.
15
Multiple Choice
Easy
1 Mark
How many straight edges does a standard cuboid box have?
A
12 straight edges
B
8 straight edges
C
6 straight edges
D
16 straight edges
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
12 straight edges
Step-by-Step Explanation:
A cuboid has 6 rectangular faces, 12 straight edges, and 8 vertices.
16
Short Answer
Hard
2 Marks
A packaging designer lines all 12 edges of a cube with reflective tape. If each edge is 15 cm long, what is the total length of reflective tape required?
A
180 cm
B
150 cm
C
160 cm
D
200 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
180 cm
Step-by-Step Explanation:
12 edges × 15 cm = 180 cm.
17
Short Answer
Hard
2 Marks
An architect builds a tower by gluing 5 cubes in a vertical stack. If each cube has 6 faces, and adjacent cubes share 1 glued face each, how many exposed outer faces does the tower have?
A
22 faces
B
25 faces
C
25 faces
D
30 faces
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
22 faces
Step-by-Step Explanation:
Each glue joint hides 2 faces. For 5 cubes, there are 4 joints hiding 8 faces: 30 - 8 = 22 exposed faces.
18
Short Answer
Hard
2 Marks
If you slice a standard solid cuboid with a single straight flat cut parallel to its base, what 2D cross-section shape is revealed?
A
A rectangle (or square)
B
A circle
C
A triangle
D
A hexagon
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
A rectangle (or square)
Step-by-Step Explanation:
Cutting parallel to the rectangular base produces a matching rectangular cross-section.
19
Short Answer
Hard
2 Marks
Why can cubes and cuboids be stacked tightly into high storage walls without gaps, while spheres leave empty space?
A
Cubes and cuboids have flat, rectangular faces that tessellate without gaps, whereas spheres only touch at single curved points
B
Spheres are too heavy to stack
C
Cubes have more mass than spheres
D
Spheres only stack when square
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Cubes and cuboids have flat, rectangular faces that tessellate without gaps, whereas spheres only touch at single curved points
Step-by-Step Explanation:
Flat parallel surfaces touch completely and distribute weight evenly, allowing gap-free tessellation in 3D.
20
Short Answer
Medium
1 Mark
Liam looks at an upright traffic cone from directly above and says: 'The top view is a triangle.' Why is Liam incorrect?
A
From directly above, a cone appears as a circle with a center point (apex), not a triangle
B
A cone appears as a square from above
C
A cone has no top view
D
Liam is right; cones always look like triangles
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
From directly above, a cone appears as a circle with a center point (apex), not a triangle
Step-by-Step Explanation:
A cone appears triangular from the front/side, but circular from directly above.
21
Short Answer
Medium
1 Mark
A student claims: 'A rectangle is always a square because both have 4 right angles.' What is the conceptual error in this statement?
A
All squares are rectangles, but not all rectangles are squares because a rectangle's adjacent sides can have different lengths
B
Rectangles have only 3 right angles
C
Squares do not have right angles
D
A rectangle has 5 sides
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
All squares are rectangles, but not all rectangles are squares because a rectangle's adjacent sides can have different lengths
Step-by-Step Explanation:
A square requires all 4 sides to be equal, which is not required for all rectangles.
22
Fill in the Blanks
Medium
1 Mark
Complete the geometry equation: [ ? ] Cubes + 1 Cylinder = 62 edges in total. How many cubes are there?
A
5 cubes
B
6 cubes
C
4 cubes
D
2 cubes
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
5 cubes
Step-by-Step Explanation:
A cylinder has 2 edges. Total - 2 = 60. Each cube has 12 edges, so 60 ÷ 12 = 5 cubes.
23
Fill in the Blanks
Medium
1 Mark
Identify the mystery solid: 'I have 0 flat faces, 0 straight edges, and 1 continuous curved surface. I can roll smoothly in any direction.'
A
Sphere
B
Cylinder
C
Cone
D
Cube
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Sphere
Step-by-Step Explanation:
A sphere has no flat faces, no straight edges, and can roll in any direction.
24
Short Answer
Medium
1 Mark
In a toy set, children assemble 4 cylindrical towers and 5 cubic blocks. How many circular flat faces are there in total on the towers?
A
8 circular faces
B
10 circular faces
C
4 circular faces
D
16 circular faces
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
8 circular faces
Step-by-Step Explanation:
Each cylinder has 2 circular faces: 4 × 2 = 8 circular faces.
25
Short Answer
Medium
1 Mark
A stage designer paints all exterior sides of 2 rectangular display boxes (cuboids). If each box has 6 flat faces, how many faces are painted across all 2 boxes?
A
12 faces
B
9 faces
C
16 faces
D
10 faces
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
12 faces
Step-by-Step Explanation:
2 × 6 faces = 12 faces.
26
Short Answer
Medium
1 Mark
At the Robotics Assembly Lab, an artisan glues 5 wooden cubes together in a straight row. How many total flat square faces were on the cubes before gluing?
A
30 flat faces
B
28 flat faces
C
34 flat faces
D
20 flat faces
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
30 flat faces
Step-by-Step Explanation:
Each cube has 6 flat faces. 5 × 6 = 30 flat faces.
27
Multiple Choice
Easy
1 Mark
What 2D shape does a soup can (cylinder) appear to be when viewed directly from the side at eye level?
A
Rectangle
B
Circle
C
Triangle
D
Oval
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Rectangle
Step-by-Step Explanation:
At exact eye level from the side, a cylinder's outline forms a rectangle.
28
Multiple Choice
Easy
1 Mark
How many flat faces and curved surfaces does an upright solid cylinder possess?
A
2 flat circular faces and 1 curved surface
B
1 flat face and 2 curved surfaces
C
3 flat faces and 0 curved surfaces
D
0 flat faces and 1 curved surface
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
2 flat circular faces and 1 curved surface
Step-by-Step Explanation:
A cylinder has 2 flat circular ends and 1 curved surface connecting them.
29
Multiple Choice
Easy
1 Mark
Which 2D shape has exactly 3 straight sides and 3 sharp corners (vertices)?
A
Triangle
B
Rectangle
C
Pentagon
D
Circle
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Triangle
Step-by-Step Explanation:
A triangle is a 3-sided polygon with 3 vertices.
30
Multiple Choice
Easy
1 Mark
How many straight edges does a standard cuboid box have?
A
12 straight edges
B
8 straight edges
C
6 straight edges
D
16 straight edges
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
12 straight edges
Step-by-Step Explanation:
A cuboid has 6 rectangular faces, 12 straight edges, and 8 vertices.
31
Short Answer
Hard
2 Marks
A packaging designer lines all 12 edges of a cube with reflective tape. If each edge is 15 cm long, what is the total length of reflective tape required?
A
180 cm
B
150 cm
C
160 cm
D
200 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
180 cm
Step-by-Step Explanation:
12 edges × 15 cm = 180 cm.
32
Short Answer
Hard
2 Marks
An architect builds a tower by gluing 4 cubes in a vertical stack. If each cube has 6 faces, and adjacent cubes share 1 glued face each, how many exposed outer faces does the tower have?
A
18 faces
B
20 faces
C
20 faces
D
24 faces
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
18 faces
Step-by-Step Explanation:
Each glue joint hides 2 faces. For 4 cubes, there are 3 joints hiding 6 faces: 24 - 6 = 18 exposed faces.
33
Short Answer
Hard
2 Marks
If you slice a standard solid cuboid with a single straight flat cut parallel to its base, what 2D cross-section shape is revealed?
A
A rectangle (or square)
B
A circle
C
A triangle
D
A hexagon
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
A rectangle (or square)
Step-by-Step Explanation:
Cutting parallel to the rectangular base produces a matching rectangular cross-section.
34
Short Answer
Hard
2 Marks
Why can cubes and cuboids be stacked tightly into high storage walls without gaps, while spheres leave empty space?
A
Cubes and cuboids have flat, rectangular faces that tessellate without gaps, whereas spheres only touch at single curved points
B
Spheres are too heavy to stack
C
Cubes have more mass than spheres
D
Spheres only stack when square
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Cubes and cuboids have flat, rectangular faces that tessellate without gaps, whereas spheres only touch at single curved points
Step-by-Step Explanation:
Flat parallel surfaces touch completely and distribute weight evenly, allowing gap-free tessellation in 3D.
35
Short Answer
Medium
1 Mark
Liam looks at an upright traffic cone from directly above and says: 'The top view is a triangle.' Why is Liam incorrect?
A
From directly above, a cone appears as a circle with a center point (apex), not a triangle
B
A cone appears as a square from above
C
A cone has no top view
D
Liam is right; cones always look like triangles
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
From directly above, a cone appears as a circle with a center point (apex), not a triangle
Step-by-Step Explanation:
A cone appears triangular from the front/side, but circular from directly above.
36
Short Answer
Medium
1 Mark
A student claims: 'A rectangle is always a square because both have 4 right angles.' What is the conceptual error in this statement?
A
All squares are rectangles, but not all rectangles are squares because a rectangle's adjacent sides can have different lengths
B
Rectangles have only 3 right angles
C
Squares do not have right angles
D
A rectangle has 5 sides
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
All squares are rectangles, but not all rectangles are squares because a rectangle's adjacent sides can have different lengths
Step-by-Step Explanation:
A square requires all 4 sides to be equal, which is not required for all rectangles.
37
Fill in the Blanks
Medium
1 Mark
Complete the geometry equation: [ ? ] Cubes + 1 Cylinder = 50 edges in total. How many cubes are there?
A
4 cubes
B
5 cubes
C
3 cubes
D
2 cubes
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
4 cubes
Step-by-Step Explanation:
A cylinder has 2 edges. Total - 2 = 48. Each cube has 12 edges, so 48 ÷ 12 = 4 cubes.
38
Fill in the Blanks
Medium
1 Mark
Identify the mystery solid: 'I have 0 flat faces, 0 straight edges, and 1 continuous curved surface. I can roll smoothly in any direction.'
A
Sphere
B
Cylinder
C
Cone
D
Cube
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Sphere
Step-by-Step Explanation:
A sphere has no flat faces, no straight edges, and can roll in any direction.
39
Short Answer
Medium
1 Mark
In a toy set, children assemble 5 cylindrical towers and 4 cubic blocks. How many circular flat faces are there in total on the towers?
A
10 circular faces
B
12 circular faces
C
5 circular faces
D
20 circular faces
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
10 circular faces
Step-by-Step Explanation:
Each cylinder has 2 circular faces: 5 × 2 = 10 circular faces.
40
Short Answer
Medium
1 Mark
A stage designer paints all exterior sides of 3 rectangular display boxes (cuboids). If each box has 6 flat faces, how many faces are painted across all 3 boxes?
A
18 faces
B
15 faces
C
22 faces
D
15 faces
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
18 faces
Step-by-Step Explanation:
3 × 6 faces = 18 faces.
41
Short Answer
Medium
1 Mark
At the Packaging Design Factory, an artisan glues 4 wooden cubes together in a straight row. How many total flat square faces were on the cubes before gluing?
A
24 flat faces
B
22 flat faces
C
28 flat faces
D
16 flat faces
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
24 flat faces
Step-by-Step Explanation:
Each cube has 6 flat faces. 4 × 6 = 24 flat faces.
42
Multiple Choice
Easy
1 Mark
What 2D shape does a soup can (cylinder) appear to be when viewed directly from the side at eye level?
A
Rectangle
B
Circle
C
Triangle
D
Oval
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Rectangle
Step-by-Step Explanation:
At exact eye level from the side, a cylinder's outline forms a rectangle.
43
Multiple Choice
Easy
1 Mark
How many flat faces and curved surfaces does an upright solid cylinder possess?
A
2 flat circular faces and 1 curved surface
B
1 flat face and 2 curved surfaces
C
3 flat faces and 0 curved surfaces
D
0 flat faces and 1 curved surface
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
2 flat circular faces and 1 curved surface
Step-by-Step Explanation:
A cylinder has 2 flat circular ends and 1 curved surface connecting them.
44
Multiple Choice
Easy
1 Mark
Which 2D shape has exactly 3 straight sides and 3 sharp corners (vertices)?
A
Triangle
B
Rectangle
C
Pentagon
D
Circle
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Triangle
Step-by-Step Explanation:
A triangle is a 3-sided polygon with 3 vertices.
45
Multiple Choice
Easy
1 Mark
How many straight edges does a standard cuboid box have?
A
12 straight edges
B
8 straight edges
C
6 straight edges
D
16 straight edges
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
12 straight edges
Step-by-Step Explanation:
A cuboid has 6 rectangular faces, 12 straight edges, and 8 vertices.
46
Short Answer
Hard
2 Marks
A packaging designer lines all 12 edges of a cube with reflective tape. If each edge is 15 cm long, what is the total length of reflective tape required?
A
180 cm
B
150 cm
C
160 cm
D
200 cm
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
180 cm
Step-by-Step Explanation:
12 edges × 15 cm = 180 cm.
47
Short Answer
Hard
2 Marks
An architect builds a tower by gluing 2 cubes in a vertical stack. If each cube has 6 faces, and adjacent cubes share 1 glued face each, how many exposed outer faces does the tower have?
A
10 faces
B
10 faces
C
10 faces
D
12 faces
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
10 faces
Step-by-Step Explanation:
Each glue joint hides 2 faces. For 2 cubes, there are 1 joints hiding 2 faces: 12 - 2 = 10 exposed faces.
48
Short Answer
Hard
2 Marks
If you slice a standard solid cuboid with a single straight flat cut parallel to its base, what 2D cross-section shape is revealed?
A
A rectangle (or square)
B
A circle
C
A triangle
D
A hexagon
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
A rectangle (or square)
Step-by-Step Explanation:
Cutting parallel to the rectangular base produces a matching rectangular cross-section.
49
Short Answer
Hard
2 Marks
Why can cubes and cuboids be stacked tightly into high storage walls without gaps, while spheres leave empty space?
A
Cubes and cuboids have flat, rectangular faces that tessellate without gaps, whereas spheres only touch at single curved points
B
Spheres are too heavy to stack
C
Cubes have more mass than spheres
D
Spheres only stack when square
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Cubes and cuboids have flat, rectangular faces that tessellate without gaps, whereas spheres only touch at single curved points
Step-by-Step Explanation:
Flat parallel surfaces touch completely and distribute weight evenly, allowing gap-free tessellation in 3D.
50
Short Answer
Medium
1 Mark
Liam looks at an upright traffic cone from directly above and says: 'The top view is a triangle.' Why is Liam incorrect?
A
From directly above, a cone appears as a circle with a center point (apex), not a triangle
B
A cone appears as a square from above
C
A cone has no top view
D
Liam is right; cones always look like triangles
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
From directly above, a cone appears as a circle with a center point (apex), not a triangle
Step-by-Step Explanation:
A cone appears triangular from the front/side, but circular from directly above.