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Shape Construction - Advanced Level: using pieces ADVANCED

Master shape construction concepts through this hard problem set practice set. Worksheet 26 of 30 contains 20 advanced-level problems. Deep dive into using pieces while learning construction puzzles, geometric design, shape formation. Recommended for advanced learners aiming for complex scenarios and multi-step problems.

📝 Worksheet 26 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

What you'll learn in this worksheet:
Your progress through Shape Construction
Worksheet 26 of 30 (86% complete)

Question 1

How many visible faces can be seen from the front view of this 3D arrangement (assuming each small cube has 6 faces, and cubes are placed on a ground plane, looking from a corner angle)? Cube arrangement (top view, 1=cube present): ⬜ ⬜ ⬜ ⬜
Each cube has 6 faces, but faces are hidden where cubes touch or touch the ground.
- Count visible faces: Top faces (1 per visible cube) + Front faces + Side faces.
- For this configuration, the total is 24 visible faces.
counting, faces, 3d, cubes

Question 2

How many visible faces can be seen from the front view of this 3D arrangement (assuming each small cube has 6 faces, and cubes are placed on a ground plane, looking from a corner angle)? Cube arrangement (top view, 1=cube present): ⬜ ⬜ ⬜
Each cube has 6 faces, but faces are hidden where cubes touch or touch the ground.
- Count visible faces: Top faces (1 per visible cube) + Front faces + Side faces.
- For this configuration, the total is 17 visible faces.
counting, faces, 3d, cubes

Question 3

If you assemble these 2D shapes in 3D space by joining matching edges, which 3D shape do you get? Parts: ▲ + ▭ + ▲
The triangular prism can be constructed from:
triangle, rectangle, triangle arranged appropriately.
This is a standard net/assembly pattern for a triangular prism.
assembly, 2d-to-3d, construction

Question 4

A standard die (opposite faces sum to 7) is shown from different angles: View 1: Top: 1 Front: 2 Right: 3 Which face is opposite to face 1?
Using the standard dice rule (opposite faces sum to 7):
- From the views, we can determine adjacency relationships
- Face 1 appears in multiple views
- Tracking orientations shows it is opposite to 6 (since 1 + 6 = 7)
dice, opposite, 3d, orientation

Question 5

This is the net of a cube with letters on each face: [A] [B][C][D] [E] [F] If face C is on top, which face is on the bottom?
By mentally folding the net:
- Identify which edges join when folded
- Track the 3D adjacency relationships
- A ends up opposite to the asked face based on the folding pattern.
cube, folding, pattern, 3d

Question 6

If you assemble these 2D shapes in 3D space by joining matching edges, which 3D shape do you get? Parts: ⚪ + ▭ + ⚪
The cylinder can be constructed from:
circle, rectangle, circle arranged appropriately.
This is a standard net/assembly pattern for a cylinder.
assembly, 2d-to-3d, construction

Question 7

This is the net of a cube with letters on each face: [A] [B][C][D] [E] [F] If face C is on top, which face is on the bottom?
By mentally folding the net:
- Identify which edges join when folded
- Track the 3D adjacency relationships
- A ends up opposite to the asked face based on the folding pattern.
cube, folding, pattern, 3d

Question 8

How many visible faces can be seen from the front view of this 3D arrangement (assuming each small cube has 6 faces, and cubes are placed on a ground plane, looking from a corner angle)? Cube arrangement (top view, 1=cube present): ⬜ ⬜ ⬜
Each cube has 6 faces, but faces are hidden where cubes touch or touch the ground.
- Count visible faces: Top faces (1 per visible cube) + Front faces + Side faces.
- For this configuration, the total is 17 visible faces.
counting, faces, 3d, cubes

Question 9

A standard die (opposite faces sum to 7) is shown from different angles: View 1: Top: 4 Front: 1 Right: 5 Which face is opposite to face 2?
Using the standard dice rule (opposite faces sum to 7):
- From the views, we can determine adjacency relationships
- Face 2 appears in multiple views
- Tracking orientations shows it is opposite to 5 (since 2 + 5 = 7)
dice, opposite, 3d, orientation

Question 10

This is the net of a cube with letters on each face: [A] [B][C][D] [E] [F] If face C is on top, which face is on the bottom?
By mentally folding the net:
- Identify which edges join when folded
- Track the 3D adjacency relationships
- A ends up opposite to the asked face based on the folding pattern.
cube, folding, pattern, 3d

Question 11

A standard die (opposite faces sum to 7) is shown from different angles: View 1: Top: 4 Front: 1 Right: 5 Which face is opposite to face 2?
Using the standard dice rule (opposite faces sum to 7):
- From the views, we can determine adjacency relationships
- Face 2 appears in multiple views
- Tracking orientations shows it is opposite to 5 (since 2 + 5 = 7)
dice, opposite, 3d, orientation

Question 12

A standard die (opposite faces sum to 7) is shown from different angles: View 1: Top: 1 Front: 2 Right: 3 Which face is opposite to face 1?
Using the standard dice rule (opposite faces sum to 7):
- From the views, we can determine adjacency relationships
- Face 1 appears in multiple views
- Tracking orientations shows it is opposite to 6 (since 1 + 6 = 7)
dice, opposite, 3d, orientation

Question 13

A standard die (opposite faces sum to 7) is shown from different angles: View 1: Top: 2 Front: 3 Right: 5 Which face is opposite to face 3?
Using the standard dice rule (opposite faces sum to 7):
- From the views, we can determine adjacency relationships
- Face 3 appears in multiple views
- Tracking orientations shows it is opposite to 4 (since 3 + 4 = 7)
dice, opposite, 3d, orientation

Question 14

If you assemble these 2D shapes in 3D space by joining matching edges, which 3D shape do you get? Parts: ⚪ + ▭ + ⚪
The cylinder can be constructed from:
circle, rectangle, circle arranged appropriately.
This is a standard net/assembly pattern for a cylinder.
assembly, 2d-to-3d, construction

Question 15

If you assemble these 2D shapes in 3D space by joining matching edges, which 3D shape do you get? Parts: ▲ + ▭ + ▲
The triangular prism can be constructed from:
triangle, rectangle, triangle arranged appropriately.
This is a standard net/assembly pattern for a triangular prism.
assembly, 2d-to-3d, construction

Question 16

If you assemble these 2D shapes in 3D space by joining matching edges, which 3D shape do you get? Parts: ▲ + ▭ + ▲
The triangular prism can be constructed from:
triangle, rectangle, triangle arranged appropriately.
This is a standard net/assembly pattern for a triangular prism.
assembly, 2d-to-3d, construction

Question 17

A standard die (opposite faces sum to 7) is shown from different angles: View 1: Top: 4 Front: 1 Right: 5 Which face is opposite to face 2?
Using the standard dice rule (opposite faces sum to 7):
- From the views, we can determine adjacency relationships
- Face 2 appears in multiple views
- Tracking orientations shows it is opposite to 5 (since 2 + 5 = 7)
dice, opposite, 3d, orientation

Question 18

A 3D structure is made of unit cubes. From the front, top, and side views: Front view (looking from front): ⬜⬜⬜ ⬜⬜⬛ ⬜⬛⬛ Top view (looking from above): ⬜⬜⬜ ⬜⬜⬛ ⬛⬛⬛ Side view (looking from right): ⬜⬜⬛ ⬜⬜⬛ ⬛⬛⬛ How many cubes are in the structure (including hidden ones)?
By reconstructing the 3D arrangement from the three orthographic views:
- Each view shows the maximum cubes in that direction
- The intersection of views reveals cube positions
- Total unique cube positions = 9 cubes
counting, hidden, 3d, orthographic

Question 19

A 3D structure is made of unit cubes. From the front, top, and side views: Front view (looking from front): ⬜⬜⬜ ⬜⬜⬛ ⬜⬛⬛ Top view (looking from above): ⬜⬜⬜ ⬜⬜⬛ ⬛⬛⬛ Side view (looking from right): ⬜⬜⬛ ⬜⬜⬛ ⬛⬛⬛ How many cubes are in the structure (including hidden ones)?
By reconstructing the 3D arrangement from the three orthographic views:
- Each view shows the maximum cubes in that direction
- The intersection of views reveals cube positions
- Total unique cube positions = 9 cubes
counting, hidden, 3d, orthographic

Question 20

A standard die (opposite faces sum to 7) is shown from different angles: View 1: Top: 4 Front: 1 Right: 5 Which face is opposite to face 2?
Using the standard dice rule (opposite faces sum to 7):
- From the views, we can determine adjacency relationships
- Face 2 appears in multiple views
- Tracking orientations shows it is opposite to 5 (since 2 + 5 = 7)
dice, opposite, 3d, orientation
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