Lesson 1.2: Views of Objects: Front, Side, and Bird's-Eye Top Views
Recognize how 3D shapes look when viewed from the top, front, and side perspectives.
⏱️ Reading Time: 15 mins
• ❓ 50 Interactive Practice Questions
🌟
Real-Life Story: Shapes and Geometry
Architect Nina designs a school library. From a drone overhead (top view), the building appears as a pair of nested rectangles. From the front street level, tall triangular glass gables become visible.
💡 Core Mathematical Concepts: Views of Objects
Focus areas: Top view (plan), front view (elevation), side view, orthographic perspective.
| Concept / Term | Mathematical Definition | Everyday Example |
|---|---|---|
| Top View (Plan View) | Looking straight down from directly above an object | Looking down on a coffee mug shows a circle with a handle sticking out |
| Front View (Front Elevation) | Looking directly at the front face at eye level | The front of a house shows the door and front windows |
| Side View (Side Elevation) | Looking directly from the left or right side at eye level | A cylinder viewed from the side looks like a rectangle |
| Orthographic Perspective | Drawing 3D objects as separate flat 2D views without angle distortion | Engineers use 3 views to manufacture machine parts |
🔍 Practical Classroom & Everyday Examples
Example 1: Top View of Solids
A sphere looks like a circle from all angles. A cone viewed from above looks like a circle with a center dot (the apex).
Example 2: Cylinder Side View
A can of soup viewed from the side at exact eye level appears as a rectangle.
⚠️ Watch Out! Common Mistakes to Avoid
Common Error: Confusing bird's-eye view with front view
Correction: Top view is looking straight down from the ceiling; front view is straight ahead at eye level.
Common Error: Assuming 3D shapes always look round
Correction: A cylinder looks round from the top but rectangular from the side.
🎯 Quick Self-Check Challenge
What 2D shape do you see when looking directly down from above onto an upright ice cream cone?
Answer & Explanation:
From directly above the apex, you see a circle with a center point (the apex).
🎯 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.