Maths

Shapes (2D and 3D Shapes)

Class 3

🎯 Learning Objectives

Identify and name 2D shapes: circle, square, rectangle, triangle, pentagon, hexagon, and oval.
Describe properties of 2D shapes — number of sides, corners (vertices), and curved/straight edges.
Identify and name 3D shapes: cube, cuboid, sphere, cylinder, and cone.
Describe properties of 3D shapes — number of faces, edges, and vertices.
Understand the difference between 2D (flat) and 3D (solid) shapes.
Recognise shapes in everyday Indian life — cricket ball, bangle, Taj Mahal, traffic cone, dice.
Identify lines of symmetry in basic shapes.

📖 Introduction

Look around your classroom, your home, and the playground. Everything you see has a shape! The clock on the wall is a circle. Your notebook is a rectangle. The slice of pizza is a triangle. A cricket ball is a sphere. A dice is a cube.

Shapes are divided into two groups: 2D shapes (flat shapes that can be drawn on paper) and 3D shapes (solid shapes that you can hold in your hands). In Class 3, we will learn more shapes like pentagon and hexagon, count faces, edges, and vertices of 3D shapes, and even discover lines of symmetry!

What Are 2D Shapes?

2D stands for two-dimensional. These shapes are flat — they have only length and breadth (width). You can draw them on paper. They have sides (straight or curved lines) and corners (also called vertices — the point where two sides meet).

Properties of 2D Shapes

Shape	Sides	Corners (Vertices)	Special Properties	Real-life Examples
Circle	0 (1 curved edge)	0	Perfectly round; all points are the same distance from the centre	Bangle, coin, wheel, roti, clock face
Oval (Ellipse)	0 (1 curved edge)	0	Like a stretched circle; longer in one direction	Egg, cricket ground, mirror, mango shape
Triangle	3	3	Fewest sides of any polygon; angles add up to 180°	Samosa, traffic yield sign, tent, slice of pizza
Square	4 (all equal)	4	All sides equal; all angles are 90° (right angles)	Carrom board, floor tile, handkerchief, chess board square
Rectangle	4 (opposite sides equal)	4	Opposite sides equal and parallel; all angles 90°	Notebook, door, TV screen, blackboard
Pentagon	5	5	Five equal sides in a regular pentagon	Some star-shaped rangoli patterns, home plate in baseball
Hexagon	6	6	Six equal sides in a regular hexagon; found in nature	Honeycomb cell, some floor tiles, nut/bolt head

Chart showing all 2D shapes — circle, square, rectangle, triangle, pentagon, hexagon with labels

Remember: A polygon is a closed shape made of straight lines. Circle and oval are NOT polygons because they have curved edges!

What Are 3D Shapes?

3D stands for three-dimensional. These shapes are solid — they have length, breadth, and height (or depth). You can pick them up and hold them. They take up space.

3D shapes have three important properties:

Faces — the flat or curved surfaces of a 3D shape
Edges — the lines where two faces meet
Vertices (corners) — the points where edges meet

Properties of 3D Shapes

Shape	Faces	Edges	Vertices	Real-life Examples
Cube	6 (all squares)	12	8	Dice, Rubik's cube, ice cube, sugar cube
Cuboid	6 (rectangles)	12	8	Brick, book, matchbox, tiffin box, eraser
Sphere	1 (curved)	0	0	Cricket ball, football, globe, marble, orange
Cylinder	3 (2 flat circles + 1 curved)	2	0	Tin can, drum, pipe, glass, candle
Cone	2 (1 flat circle + 1 curved)	1	1 (apex/tip)	Ice cream cone, traffic cone, birthday cap, funnel

3D shapes with matching real-life objects — cube, sphere, cylinder, cone, cuboid

🔍 How to Count Faces, Edges, and Vertices

Example: Cube (like a dice)

Pick up a dice. Count the flat surfaces → 6 faces (top, bottom, front, back, left, right)
Run your finger along the lines where two faces meet → 12 edges
Touch the pointed corners → 8 vertices

Example: Cone (like a birthday cap)

It has 1 flat circular face at the bottom and 1 curved surface
The curved surface meets the flat face along 1 circular edge
The pointed tip at the top is 1 vertex (apex)

A cube is a special cuboid where ALL faces are squares. Just like a square is a special rectangle!

Difference Between 2D and 3D Shapes

Feature	2D Shapes (Flat)	3D Shapes (Solid)
Dimensions	Length and breadth only	Length, breadth, and height
Can you draw it on paper?	Yes	No (only a picture of it)
Can you hold it?	No (it's flat)	Yes (it takes up space)
Parts	Sides and corners (vertices)	Faces, edges, and vertices
Examples	Circle, square, triangle, rectangle, pentagon, hexagon	Cube, cuboid, sphere, cylinder, cone
Thickness	No thickness	Has thickness/depth

Think of it this way: A 2D shape is like a shadow on the wall. A 3D shape is the actual object that makes the shadow!

Shapes in Everyday Indian Life

Shapes are all around us! Here are some shapes you can spot in your daily life in India:

Object	Shape	Type
Cricket ball	Sphere	3D
Dice (ludo game)	Cube	3D
Bangle (चूड़ी)	Circle	2D shape of the ring
Traffic cone on roads	Cone	3D
Taj Mahal dome	Hemisphere (half sphere) on a cuboid base	3D
Roti / Chapati	Circle	2D (flat)
Samosa	Triangle (roughly)	3D (triangular pyramid)
Diya (oil lamp)	Cone-like	3D
Honeycomb	Hexagons	2D pattern
Stop sign / Yield sign	Hexagon / Triangle	2D
Drum (dholak)	Cylinder	3D
Book / Notebook	Cuboid	3D

Shapes found in Indian daily life — rangoli, windows, wheels, road signs

Lines of Symmetry

A line of symmetry is an imaginary line that divides a shape into two equal halves that are mirror images of each other. If you fold the shape along this line, both halves will match exactly.

Lines of Symmetry in 2D Shapes

Shape	Lines of Symmetry	Explanation
Circle	Infinite (unlimited)	You can fold a circle along any line through its centre
Square	4	2 through opposite corners (diagonals) + 2 through midpoints of opposite sides
Rectangle	2	1 horizontal (through midpoints of longer sides) + 1 vertical (through midpoints of shorter sides)
Equilateral Triangle	3	Each line goes from a vertex to the midpoint of the opposite side
Regular Pentagon	5	Each line goes from a vertex to the midpoint of the opposite side
Regular Hexagon	6	3 through opposite vertices + 3 through midpoints of opposite sides
Oval	2	1 along the longer axis + 1 along the shorter axis

🪞 Try This!

Take a square piece of paper. Fold it in half from top to bottom — both halves match! Now fold it from left to right — they match again! Now fold along a diagonal — still matching! A square has 4 lines of symmetry.

Now take a rectangular piece of paper. Fold it top to bottom — matches! Left to right — matches! But fold along a diagonal — the halves do NOT match. A rectangle has only 2 lines of symmetry.

Relationship Between 2D and 3D Shapes

Every 3D shape is made up of 2D shapes! The faces of a 3D shape are 2D shapes:

3D Shape	2D Shapes in Its Faces
Cube	6 squares
Cuboid	6 rectangles (or 4 rectangles + 2 squares)
Cylinder	2 circles (top and bottom)
Cone	1 circle (base)
Sphere	No flat face (all curved)

If you trace around the bottom of a cylinder on paper, you get a circle. If you trace around the face of a cube, you get a square!

Rolling and Sliding

Some 3D shapes can roll (because they have curved surfaces) and some can only slide (because they have only flat surfaces).

Shape	Can Roll?	Can Slide?	Why?
Sphere	Yes (any direction)	No	Entirely curved surface
Cylinder	Yes (one direction)	Yes	Has curved + flat surfaces
Cone	Yes (in a circle)	Yes	Has curved + flat surfaces
Cube	No	Yes	Only flat surfaces
Cuboid	No	Yes	Only flat surfaces

📝 Key Words

Word	Meaning
2D (Two-dimensional)	A flat shape with only length and breadth; can be drawn on paper
3D (Three-dimensional)	A solid shape with length, breadth, and height; takes up space
Side	A straight line that forms part of a 2D shape
Vertex (plural: Vertices)	A corner — the point where two sides or edges meet
Face	A flat or curved surface of a 3D shape
Edge	The line where two faces of a 3D shape meet
Polygon	A closed 2D shape made of straight lines (triangle, square, pentagon, etc.)
Line of Symmetry	A line that divides a shape into two equal mirror-image halves
Pentagon	A polygon with 5 sides and 5 vertices
Hexagon	A polygon with 6 sides and 6 vertices
Apex	The pointed tip of a cone or pyramid

⭐ Key Points to Remember

2D shapes are flat (circle, square, rectangle, triangle, pentagon, hexagon, oval). 3D shapes are solid (cube, cuboid, sphere, cylinder, cone).
A circle has 0 sides and 0 corners. A triangle has 3 sides and 3 corners. A square has 4 equal sides. A pentagon has 5 sides. A hexagon has 6 sides.
3D shapes have faces (surfaces), edges (where faces meet), and vertices (corners).
A cube has 6 faces, 12 edges, and 8 vertices. A sphere has 1 curved face, 0 edges, and 0 vertices.
2D shapes have length and breadth. 3D shapes have length, breadth, and height.
Shapes with curved surfaces can roll. Shapes with only flat surfaces can only slide.
A line of symmetry divides a shape into two equal mirror halves. A circle has infinite lines of symmetry. A square has 4. A rectangle has 2.
The faces of 3D shapes are 2D shapes (cube faces are squares, cuboid faces are rectangles).

Finished learning? Now test what you know!

🎯 Quick Quiz — Test Yourself!

Answer these questions right here. You get instant feedback — no paper needed!

Score: 0 / 8

1. How many sides does a triangle have?

A triangle has 3 sides and 3 corners.

2. A shape with 4 equal sides is a:

A square has 4 equal sides.

3. A ball and a globe are examples of which 3D shape?

A ball and globe are spheres — perfectly round 3D shapes.

4. A dice (like in Ludo) is which 3D shape?

A dice is a cube — it has 6 square faces.

5. Which flat shape is perfectly round with no corners?

A circle is round and has no sides or corners.

6. How many corners does a rectangle have?

A rectangle has 4 corners and 4 sides.

7. An ice-cream cone and a party hat are examples of which 3D shape?

An ice-cream cone and party hat are cones.

8. A tin can and a Bournvita jar are examples of which 3D shape?

A tin can and a jar are cylinders.

✏️ Practice Questions

A. Fill in the Blanks (10)

1. A pentagon has sides and corners.

2. A cube has faces, edges, and vertices.

3. A shape that has length, breadth, and height is called a shape.

4. A cricket ball is shaped like a .

5. A hexagon has sides.

6. The point where two edges of a 3D shape meet is called a .

7. A cylinder has flat faces and curved surface.

8. A square has lines of symmetry.

9. The flat surface of a 3D shape is called a .

10. A can roll in any direction because it is entirely curved.

B. Choose the Correct Answer (MCQ - 5)

1. How many edges does a cuboid have?

a) 6b) 8c) 12d) 4

2. Which shape has 6 sides?

a) Pentagonb) Hexagonc) Squared) Triangle

3. How many lines of symmetry does a rectangle have?

a) 1b) 2c) 4d) 0

4. Which 3D shape has only 1 vertex?

a) Cubeb) Cylinderc) Coned) Sphere

5. A dice is an example of which shape?

a) Cuboidb) Cubec) Sphered) Cylinder

C. Short Answer Questions (5)

1. What is the difference between a 2D shape and a 3D shape? Give one example of each.

2. Name three objects in your home that are shaped like a cuboid.

3. Why can a sphere roll in any direction but a cylinder can only roll in one direction?

4. How many lines of symmetry does a square have? Name them.

5. What 2D shapes make up the faces of a cube? How many faces does it have?

D. True or False (5)

1. A cone has 2 edges.

2. A hexagon has 6 lines of symmetry.

3. A sphere has no vertices and no edges.

4. A rectangle has 4 lines of symmetry.

5. The faces of a cuboid are all rectangles.

E. Match the Following (5)

Object	Shape
1. Honeycomb cell	a) Sphere
2. Globe	b) Cylinder
3. Drum (dholak)	c) Hexagon
4. Traffic cone	d) Cuboid
5. Brick	e) Cone

🎨 Activity: Shape Detective

Materials needed: A notebook, pencil, and objects from around your home.

Instructions:

Walk around your home and find at least 2 objects for each 3D shape: cube, cuboid, sphere, cylinder, and cone.
For each object, write its name, draw it, and write how many faces, edges, and vertices it has.
Now take a square piece of paper. Fold it to find all 4 lines of symmetry. Draw dotted lines where you folded.
Take a rectangular piece of paper. Can you find its 2 lines of symmetry? Try folding along the diagonal — does it work?
Make a table in your notebook: Object | Shape | Faces | Edges | Vertices

Want to review the lesson again?

Mathematics

Shapes (2D and 3D Shapes)

Class 3 | CBSE / NCERT / ICSE

Name: Class: Date:

Learning Objectives

Identify and name 2D shapes: circle, square, rectangle, triangle, pentagon, hexagon, oval.
Describe properties of 2D shapes — sides, corners (vertices).
Identify and name 3D shapes: cube, cuboid, sphere, cylinder, cone.
Describe properties of 3D shapes — faces, edges, vertices.
Understand the difference between 2D and 3D shapes.
Recognise shapes in everyday Indian life.
Identify lines of symmetry in basic shapes.

Introduction

Look around your classroom, home, and playground. Everything has a shape! The clock is a circle. Your notebook is a rectangle. A pizza slice is a triangle. A cricket ball is a sphere. A dice is a cube. Shapes are divided into 2D shapes (flat) and 3D shapes (solid). In Class 3, we learn pentagon, hexagon, faces, edges, vertices, and lines of symmetry!

2D Shapes (Flat Shapes)

2D = two-dimensional. Flat shapes with length and breadth only. Have sides and corners (vertices).

Shape	Sides	Corners	Special Properties	Examples
Circle	0 (curved)	0	Perfectly round	Bangle, coin, wheel, roti
Oval	0 (curved)	0	Stretched circle	Egg, cricket ground, mirror
Triangle	3	3	Fewest sides of any polygon	Samosa, traffic sign, tent
Square	4 (all equal)	4	All sides equal, all angles 90°	Carrom board, tile, chess square
Rectangle	4	4	Opposite sides equal, angles 90°	Notebook, door, TV screen
Pentagon	5	5	Five-sided polygon	Rangoli patterns
Hexagon	6	6	Six-sided; found in nature	Honeycomb, bolt head

3D Shapes (Solid Shapes)

3D = three-dimensional. Solid shapes with length, breadth, and height. Have faces, edges, and vertices.

Shape	Faces	Edges	Vertices	Examples
Cube	6 (squares)	12	8	Dice, Rubik's cube, ice cube
Cuboid	6 (rectangles)	12	8	Brick, book, matchbox, eraser
Sphere	1 (curved)	0	0	Cricket ball, globe, marble
Cylinder	3 (2 flat + 1 curved)	2	0	Tin can, drum, pipe, candle
Cone	2 (1 flat + 1 curved)	1	1 (apex)	Ice cream cone, traffic cone, cap