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Shape Construction - Intermediate-Advanced Level: geometric design INTERMEDIATE-ADVANCED

This fundamentals focus worksheet contains 20 intermediate-advanced-level shape construction problems. Worksheet 21 of 30 focuses on geometric design. Practice shape formation, tile assembly, shape construction with our step-by-step solutions. Difficulty: advanced concepts with increasing complexity. Recommended for advanced developing learners.

📝 Worksheet 21 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate-advanced level

What you'll learn in this worksheet:
Your progress through Shape Construction
Worksheet 21 of 30 (70% complete)

Question 1

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 2

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 3

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 4

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 = 7 cubes
counting, hidden, 3d, orthographic

Question 5

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 22 visible faces.
counting, faces, 3d, cubes

Question 6

Which of the following nets can be folded into a cube (without overlapping)?
A valid cube net must have exactly 6 squares connected edge-to-edge, with each square adjacent to at most 4 others, and when folded, all squares meet at edges without overlap.
This net is one of the 11 known cube nets.
cube, net, folding, 3d

Question 7

Which of the following nets can be folded into a cube (without overlapping)?
A valid cube net must have exactly 6 squares connected edge-to-edge, with each square adjacent to at most 4 others, and when folded, all squares meet at edges without overlap.
This net is one of the 11 known cube nets.
cube, net, folding, 3d

Question 8

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 9

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 10

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 11

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 18 visible faces.
counting, faces, 3d, cubes

Question 12

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 22 visible faces.
counting, faces, 3d, cubes

Question 13

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 14

Which of the following nets can be folded into a cube (without overlapping)?
A valid cube net must have exactly 6 squares connected edge-to-edge, with each square adjacent to at most 4 others, and when folded, all squares meet at edges without overlap.
This net is one of the 11 known cube nets.
cube, net, folding, 3d

Question 15

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

Question 16

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 17

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 18

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 19

Which of the following nets can be folded into a cube (without overlapping)?
A valid cube net must have exactly 6 squares connected edge-to-edge, with each square adjacent to at most 4 others, and when folded, all squares meet at edges without overlap.
This net is one of the 11 known cube nets.
cube, net, folding, 3d

Question 20

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 22 visible faces.
counting, faces, 3d, cubes
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