3D Objects and Their Nets
Match 3D Shapes to Names
Draw a line from each description to its name.
Match 3D Shapes to Real Objects
Draw a line from each shape to a real object.
Faces, Edges and Vertices (A)
Circle the correct answer.
How many faces does a cube have?
How many edges does a rectangular prism have?
How many vertices does a triangular pyramid have?
How many faces does a cylinder have?
Faces, Edges and Vertices (B)
Circle the correct answer.
How many edges does a cube have?
How many vertices does a rectangular prism have?
How many faces does a triangular prism have?
A sphere has ___ vertices.
Sort by Shape Type
Sort each object.
Describe 3D Shapes
Fill in the table for each shape.
Cube: ___ faces, ___ edges, ___ vertices
Rectangular prism: ___ faces, ___ edges, ___ vertices
Triangular prism: ___ faces, ___ edges, ___ vertices
Square pyramid: ___ faces, ___ edges, ___ vertices
Euler's Rule: V + F = E + 2
For 3D shapes: Vertices + Faces = Edges + 2. Find the missing value.
Match Objects to Nets (A)
Draw a line from each 3D object to the description of its net.
Match Objects to Nets (B)
Match each object to its net description.
Will This Net Work? (A)
Circle YES or NO.
Can 6 squares in a cross shape fold into a cube?
Can 4 squares in a row fold into a cube?
Can a square + 4 triangles fold into a pyramid?
Can 6 squares in a straight line fold into a cube?
Will This Net Work? (B)
Circle YES or NO.
Can 5 squares in a T-shape fold into an open box?
Can 4 squares in an L-shape + 2 squares fold into a cube?
Can 2 triangles + 3 squares fold into a triangular prism?
Identify the Net
What 3D shape would each net make?
A net with 6 identical squares: ___
A net with 1 square base and 4 triangles: ___
A net with 2 circles and 1 rectangle: ___
A net with 2 triangles and 3 rectangles: ___
Sort: Net Has Curved or Flat Faces Only?
Sort each 3D shape.
Count the Faces in Each Net
How many faces are in the net for each shape?
Cube net: ___ faces
Triangular prism net: ___ faces
Square pyramid net: ___ faces
Rectangular prism net: ___ faces
Draw the Net (A)
In each box, draw a possible net for the 3D shape.
Draw a net for a rectangular prism (box shape).
Draw a net for a triangular pyramid (tetrahedron).
Draw TWO different nets that could fold into a cube.
Draw the Net (B)
Draw nets for these shapes.
Draw a net for a triangular prism.
Draw a net for a square pyramid.
Net Investigation
Answer these questions about cube nets.
There are 11 different nets that fold into a cube. Can you find at least 5? Draw them.
Explain why 6 squares in a straight line cannot fold into a cube.
3D Shape Problems
Solve these problems.
A box is 10 cm long, 6 cm wide and 4 cm tall. If you unfold it into a net, how many rectangular faces are there? What are their dimensions?
A cube has a side length of 5 cm. What is the total area of all its faces (surface area)?
Real-World Nets
Think about packaging and nets.
What 3D shape is a Toblerone box? Describe its net.
What 3D shape is a party hat? Describe its net.
Design a box (rectangular prism) to hold a gift. Write the dimensions and describe the net.
Match 3D Shapes to Face Shapes
Draw a line from each 3D shape to the shapes of its faces.
Faces, Edges and Vertices (C)
Circle the correct answer.
A cone has ___ vertex/vertices.
A triangular prism has ___ edges.
A rectangular prism has ___ faces.
A square pyramid has ___ edges.
Faces, Edges and Vertices (D)
Circle the correct answer.
A triangular pyramid has ___ faces.
A hexagonal prism has ___ faces.
A pentagonal prism has ___ vertices.
A cylinder has ___ edges.
Sort by Number of Faces
Sort each 3D shape.
Describe 3D Shapes (B)
Fill in the properties.
Cone: ___ flat face(s), ___ curved surface(s), ___ vertex/vertices
Cylinder: ___ flat face(s), ___ curved surface(s), ___ vertex/vertices
Sphere: ___ flat face(s), ___ curved surface(s), ___ vertex/vertices
Triangular pyramid: ___ faces, ___ edges, ___ vertices
Euler's Rule (B): V + F = E + 2
Use Euler's Rule. Find the missing value.
Match 3D Shapes to Properties
Draw a line.
Match Objects to Nets (C)
Match each 3D object to its net.
Will This Net Work? (C)
Circle YES or NO.
Can a T-shaped arrangement of 6 squares fold into a cube?
Can 2 triangles and 3 rectangles fold into a triangular prism?
Can 3 squares in a row fold into a cube?
Can 4 equilateral triangles fold into a triangular pyramid?
Will This Net Work? (D)
Circle YES or NO.
Can 6 squares arranged in a plus (+) shape fold into a cube?
Can 5 triangles fold into a square pyramid?
Can 1 circle and 1 triangle fold into a cone?
Can 2 circles and 2 rectangles fold into a cylinder?
Identify the Net (B)
What 3D shape would each net make?
A net with 4 equilateral triangles: ___
A net with 1 circle and 1 sector (fan shape): ___
A net with 2 pentagons and 5 rectangles: ___
A net with 1 hexagon and 6 triangles: ___
Count Faces in Nets (B)
How many flat faces are in each net?
Cone net: ___ flat face(s) + ___ curved piece(s)
Hexagonal prism net: ___ faces
Pentagonal pyramid net: ___ faces
Octahedron net (8 triangles): ___ faces
Sort: Prism, Pyramid or Other?
Sort each 3D shape.
Cross-Sections
What 2D shape do you see if you slice each 3D shape?
Slice a cube straight across the middle: ___
Slice a cylinder straight across: ___
Slice a sphere through the centre: ___
Slice a square pyramid half way up, parallel to the base: ___
Match Cross-Sections
Draw a line from each 3D shape to its cross-section shape.
Draw the Net (C)
Draw nets for these shapes.
Draw a net for a hexagonal prism (2 hexagons + 6 rectangles).
Draw a different net for a cube that is NOT the cross shape.
Surface Area from Nets (A)
Use the net to calculate surface area.
A cube has side length 4 cm. Each face area = ___. Total surface area = 6 × ___ = ___ cm²
A rectangular prism is 6 cm × 4 cm × 3 cm. Find the area of each pair of faces and add them up.
Surface Area from Nets (B)
Calculate surface area.
A cube with side 10 cm. Surface area = ___
A rectangular prism 5 cm × 3 cm × 2 cm. Surface area = ___
Which has the greater surface area: a cube with side 3 cm, or a rectangular prism 4 cm × 3 cm × 1 cm?
Net Investigation (B)
Investigate these questions.
Can you draw a net for a cylinder? What shapes make up the net?
If you cut a cereal box along its edges to make a net, how many different nets could you make?
Explain why a sphere does NOT have a net.
3D Shape Reasoning
Circle the correct answer.
Which 3D shape has the most faces from these options?
Which shape has no edges?
All prisms have...
Euler's rule V + F - E = ?
Design a Package
Design packaging using nets.
Design a gift box shaped like a triangular prism. Give dimensions and describe the net.
A chocolate box is shaped like a hexagonal prism. How many faces does the net have? Draw a rough sketch.
Match Faces, Edges and Vertices (A)
Draw a line from each 3D shape to its vertex count.
Faces, Edges and Vertices (E)
Circle the correct answer.
How many edges does a triangular pyramid have?
How many faces does a hexagonal prism have?
How many vertices does a pentagonal pyramid have?
A cube and a rectangular prism both have ___ edges.
Euler's Rule (C): V + F - E = 2
Use Euler's Rule (V + F = E + 2). Find the missing value.
Sort by Number of Vertices
Sort each 3D shape.
Describe 3D Shapes (C)
Fill in the properties.
Hexagonal prism: ___ faces, ___ edges, ___ vertices
Pentagonal pyramid: ___ faces, ___ edges, ___ vertices
Octahedron (8 faces): ___ faces, ___ edges, ___ vertices
Identify the Net (C)
What 3D shape would each net make?
A net with 2 pentagons and 5 rectangles: ___
A net with 8 equilateral triangles: ___
A net with 2 hexagons and 6 rectangles: ___
A net with 6 identical rectangles (no equal pairs): ___
Match 3D Shapes to Nets (D)
Draw a line.
Will This Net Work? (E)
Circle YES or NO.
Can 5 squares form a valid cube net if arranged in a Z-shape?
Can 6 squares in an S-shape fold into a cube?
Can 3 rectangles + 2 triangles fold into a triangular prism?
Can a triangle + 3 rectangles fold into a triangular pyramid?
3D Shapes in Architecture
Count 3D shapes in a building survey.
| Rectangular prisms | |
| Cylinders | |
| Cones | |
| Spheres |
Most common shape?
Total shapes counted?
What fraction are rectangular prisms?
Why are prisms so common in buildings?
Net Types Survey
Students identified net types. Count results.
| Item | Tally | Total |
|---|---|---|
Cube net | ||
Pyramid net | ||
Prism net | ||
Cylinder net |
Surface Area from Nets (C)
Calculate surface area.
A triangular prism with triangular end (base 6 cm, height 4 cm) and length 10 cm. The two triangles' area = ___. The three rectangles' area = ___. Total surface area = ___
3D Shapes in Food Packaging
Think about real packaging.
Name 3 food items that come in a rectangular prism package: ___, ___, ___
Name 2 food items in a cylinder: ___, ___
Name 1 food item in a cone or cone-like shape: ___
Why do you think most food is packaged in rectangular prisms?
Net Problems
Solve these net problems.
A cereal box is 30 cm × 8 cm × 22 cm. What is the total surface area of the box? (Find the area of each face.)
If you wanted to wrap the cereal box in paper with no overlap, what is the minimum area of paper needed?
3D Shape Investigation
Investigate prisms and pyramids.
How is a prism different from a pyramid? ___
Both a triangular prism and a triangular pyramid start with a triangle. What makes them different?
Can you have a circular prism? What would it be called?
3D Shapes Quiz (B)
Circle the correct answer.
Prisms have two ___ faces.
Pyramids come to a ___.
A cone is like a ___ with a circular base.
A tetrahedron has ___ faces.
Match 3D Shapes to Number of Edges (B)
Draw a line.
Euler's Formula Practise
For every 3D shape: Vertices + Faces = Edges + 2.
Describe the Cross-Section (B)
What 2D shape do you see if you cut each 3D shape?
Cut a triangular prism across its length: ___
Cut a square pyramid half way up: ___
Cut a cube diagonally corner-to-corner: ___
Cut a cylinder along its length: ___
Properties Comparison Table
Complete the table comparing 3D shapes.
Shape: Cube. Faces: ___. Edges: ___. Vertices: ___. Face shapes: ___
Shape: Triangular prism. Faces: ___. Edges: ___. Vertices: ___. Face shapes: ___
Shape: Square pyramid. Faces: ___. Edges: ___. Vertices: ___. Face shapes: ___
Sort: How Many Vertices?
Sort each 3D shape.
Net Identification (B)
Circle the correct shape the net makes.
Two equilateral triangles + 3 rectangles →
6 equal squares →
1 circle + 1 sector (fan) →
5 squares arranged in a plus (+) → (only 5 squares total)
Design a Product Package
Design packaging for a product.
Choose a product (e.g. chocolates, dice). What 3D shape would best package it?
Describe the net for your package. How many faces? What shapes are they?
Give the dimensions of your package: length ___ width ___ height ___
3D Shapes in Everyday Life
Students counted 3D shapes in their house.
| Boxes | |
| Cans (cylinders) | |
| Balls (spheres) | |
| Cone shapes |
Most common shape at home?
Total shapes counted?
What fraction are boxes?
Why are most containers boxes or cylinders?
Faces on 3D Shapes
Count the total faces for each shape type.
| Item | Tally | Total |
|---|---|---|
Cube (6 faces) | ||
Triangular prism (5) | ||
Cylinder (3) | ||
Pyramid (5) |
Origami and Nets
Explore the connection between folding and nets.
How is making origami similar to folding a net?
What shape would you get if you folded all the flaps of a cereal box flat? ___
Design a gift box that is NOT a rectangular prism. What 3D shape did you choose? Describe its net.
Challenge: How Many Valid Cube Nets?
There are exactly 11 different nets that fold into a cube.
Draw 3 different valid cube nets:
Draw 1 arrangement of 6 squares that does NOT fold into a cube and explain why:
Compare 3D Shapes
Which shape has more?
Cube or triangular prism: more faces?
Cube or triangular prism: more edges?
Cube or triangular prism: more vertices?
Match 3D Shape to Net Description
Draw a line.
Face Count Bonds for 3D Shapes
Find the missing number of faces, edges, or vertices using Euler's rule.
Identify the Net (B)
Circle the correct 3D shape the net makes.
Net with 2 circles and 1 rectangle folds into a...
Net with 2 triangles and 3 rectangles folds into a...
Net with 1 square and 4 triangles folds into a...
Net with 6 squares all equal folds into a...
Sort 3D Shapes: Prism or Pyramid?
Sort each shape.
Cross-Sections of 3D Shapes (B)
Describe or draw cross-sections.
If you slice a cylinder horizontally: ___. Vertically: ___
If you slice a cube diagonally from edge to edge: ___
If you slice a cone horizontally near the top: ___. Near the base: ___
Properties Table for 3D Shapes
Complete the properties table.
Cube: Faces=___ Edges=___ Vertices=___. Verify with Euler's rule:
Triangular prism: Faces=___ Edges=___ Vertices=___. Verify:
Square pyramid: Faces=___ Edges=___ Vertices=___. Verify:
Face-Edge-Vertex Sequences
These show faces of prisms (triangular, square, pentagon...). Continue.
Compare 3D Shapes
Tick which has more.
Cube (6 faces) vs triangular prism (5 faces)
Cube (12 edges) vs triangular prism (9 edges)
Net for a Triangular Prism (B)
Draw and label the net for a triangular prism.
A triangular prism has dimensions: triangle base 4 cm, height 3 cm, length 8 cm. Draw the net:
Label the faces. How many faces are rectangles? ___ How many are triangles? ___
Surface area: 2 triangles + 3 rectangles = ___
Flat Packing 3D Shapes
Engineers and manufacturers need to pack 3D shapes flat.
How does knowledge of nets help in manufacturing boxes? ___
Why is a rectangular box easier to flat-pack than a sphere? ___
Design a net for a package to hold a single tennis ball: ___
3D Shapes in Food Packaging (B)
Analyse 3D shapes used in food packaging.
Name 3 foods that come in a cylinder-shaped container: ___, ___, ___
Why might a cylinder be preferred over a box for some products? ___
Sketch the net of a soup can (cylinder): show the two circles and the rectangle.
Prism and Pyramid Comparison (B)
Compare prisms and pyramids.
A hexagonal prism: faces=___ edges=___ vertices=___. Verify with Euler's rule:
A hexagonal pyramid: faces=___ edges=___ vertices=___. Verify:
What is the key difference between a prism and a pyramid of the same base?
Build a 3D Model Plan
Plan a 3D model project.
Choose a real-life structure (house, barn, lighthouse). Describe the 3D shapes it uses:
How would you build this using nets? Describe the shapes you need to cut:
Sketch the net for the main body of your structure:
Volume Introduction
Volume measures 3D space inside a shape.
Volume of a cube = side³. Volume of a cube with side 4 cm: ___
Volume of a rectangular prism = L × W × H. For 5 cm × 3 cm × 2 cm: ___
How is volume different from surface area? ___
3D Shapes True or False (B)
Circle TRUE or FALSE.
A cone has 2 faces (1 circle + 1 curved)
A sphere has 0 edges and 0 vertices
All prisms have at least 5 faces
A pyramid and a prism can have the same base shape
3D Shape Properties (C)
Match each 3D shape to its number of faces.
Euler's Formula: V + F − E = 2
Fill in the missing value.
Net or Not a Net?
Circle YES if it would fold into a cube, NO if not.
Cross shape (1×4 row + 2 extra): makes a cube?
L-shape of 6 squares: makes a cube?
A flat strip of 4 squares in a row: makes a cube?
There are 11 different nets for a cube
Sort 3D Shapes: Prism or Pyramid?
Sort each shape.
Cross-Sections of 3D Shapes (C)
Describe what you see when you cut a 3D shape.
Cutting a cube in half parallel to a face gives a: ___
Cutting a square pyramid through its apex gives a: ___
Cutting a cylinder along its length gives a: ___
Which 3D shape gives a circle when cut in any direction? ___
Surface Area of a Rectangular Prism
Calculate surface area.
A box is 6 cm × 4 cm × 3 cm. Draw the net and label dimensions:
Area of each face pair: Top/bottom: ___ × 2 = ___. Front/back: ___ × 2 = ___. Sides: ___ × 2 = ___. Total SA: ___
3D Shape Face Sequences
Extend the pattern: prisms with n-gon base have how many faces?
Compare Surface Areas
Which has more surface area?
Cube 2×2×2 (SA=24) vs rectangular prism 3×2×1 (SA=22) — which is more?
Square pyramid 4×4 base h=3 vs triangular prism — surface area comparison
3D Shapes in the Classroom
Count 3D shapes found in the classroom.
| Item | Tally | Total |
|---|---|---|
Rectangular prisms (boxes) | ||
Cylinders | ||
Spheres | ||
Other shapes |
Faces on Different Prisms
Each icon = 1 face. Count faces per shape.
| Triangular prism | |
| Rectangular prism | |
| Pentagonal prism | |
| Hexagonal prism |
Pattern: faces = sides + ___
Total faces across all shapes?
Which has the most faces?
How many faces would an octagonal prism have?
Visualising 3D Shapes from 2D Drawings
Identify 3D shapes from their 2D drawings.
A drawing shows a circle with a triangle on top connecting to the center. What 3D shape is this? ___
A drawing shows a rectangle with two equal triangles on each end. What 3D shape? ___
Draw the 2D top view (plan) and front view (elevation) of a rectangular prism:
3D Shapes in Technology and Design
Think about 3D shapes in the real world.
Name the 3D shapes used in these structures: pyramid building: ___, dome roof: ___, grain silo: ___
3D printing creates objects layer by layer. How is this related to cross-sections? ___
Describe a real-world object that uses at least two different 3D shapes:
Nets and Real-World Packaging Design
Connect nets to packaging.
A cereal box is 30 cm × 20 cm × 8 cm. Draw its net and label dimensions:
Calculate the total surface area of cardboard needed: ___
Why might a company want to minimise surface area in packaging design?
3D Shape Challenge Questions
Apply your 3D knowledge.
A cube has V=8, E=12, F=6. Verify Euler's rule: V + F − E = ___
Add a point on top of a cube to make a square pyramid on top. New V=___ E=___ F=___. Verify Euler's rule: ___
Which 3D shape has the fewest edges and faces? ___
Home Activity: Build from Nets
Make 3D shapes from nets!
- 1Draw a cube net on cardboard. Cut it out and fold it into a cube.
- 2Cut open a cereal box carefully along its edges. Lay it flat — you have found its net!
- 3Try to draw and cut out a net for a triangular prism.
- 4Collect different boxes and packaging. Predict what shape their net would be before unfolding them.