NCERT Class 4 Maths · Chapter 1
Shapes Around Us
3D shapes (cubes, prisms, pyramids, cylinders, cones), nets, faces, edges and corners, angles, and circles.
📌 What you’ll learn in this chapter
- Names of 3D shapes, and how to count their faces, edges, and corners
- Prisms and pyramids, and what makes them different
- Nets: the flat, opened-out form of a box
- Angles: right, acute, and obtuse
- Circles: centre, radius, and diameter
🏛️ Let’s Begin: Building a Monument
Aryan visited the Red Fort in Delhi with his family. Back home, he built it with things from the kitchen: a big biscuit box for the wall, matchboxes for the gates, and ice-cream cones turned upside down for the domes!
Every building is made of simple shapes. Let’s learn their names.
📦 Part 1: 3D Shapes Around Us
| Shape | Everyday example | Faces | Edges | Corners |
|---|---|---|---|---|
| Cube | Dice, Rubik’s cube | 6 squares | 12 | 8 |
| Cuboid | Brick, matchbox, lunch box | 6 rectangles | 12 | 8 |
| Cylinder | Pipe, candle, glass | 2 flat + 1 curved | 2 (curved) | 0 |
| Cone | Ice-cream cone, birthday cap | 1 flat + 1 curved | 1 (curved) | 0 (1 tip) |
| Sphere | Ball, laddoo, orange | 1 curved | 0 | 0 |
| Square pyramid | Pyramids of Egypt | 5 | 8 | 5 |
| Triangular prism | Tent, Toblerone box | 5 | 9 | 6 |
💡 Words to know
Face = a flat or curved surface · Edge = where two faces meet · Corner (vertex) = where edges meet
Prisms and pyramids
- A prism has two same ends (triangles, squares, hexagons…), and its side faces are rectangles. A cube is also a prism!
- A pyramid has one base, and its side faces are triangles that meet at one top point.
Magic rule: For shapes with flat faces, Faces + Corners − Edges = 2.
Cube: 6 + 8 − 12 = 2 ✅ · Square pyramid: 5 + 5 − 8 = 2 ✅ · Triangular prism: 5 + 6 − 9 = 2 ✅
✂️ Part 2: Nets
Carefully open a toothpaste box and lay it flat. The flat shape you get is its net. Fold it back along the lines and you get the box again!
- Cube net: 6 squares
- Cylinder net: 1 rectangle + 2 circles
- Square pyramid net: 1 square + 4 triangles
- Triangular prism net: 3 rectangles + 2 triangles
⚠️ Common mistake
Thinking any 6 squares joined together make a cube. ❌
✅ Six squares in a straight line can’t fold into a cube. Cut the net out and try folding it to check!
✅ Six squares in a straight line can’t fold into a cube. Cut the net out and try folding it to check!
📐 Part 3: Angles
When two lines meet at a point, they make an angle. You can see angles in scissors, a clock’s hands, and the corners of a book.
Make a right angle checker: fold a paper in half, then fold it in half again. The folded corner is a perfect right angle.
| Angle | Compared to the checker | Example |
|---|---|---|
| Right angle | Fits exactly | Corner of a book or door |
| Acute angle | Smaller (fits inside) | Tip of a pizza slice, a partly open scissors |
| Obtuse angle | Bigger (wider) | An open laptop leaning back, a reclining chair |
Straw fun: Push a straw triangle, and it doesn’t change shape (strong!). Push a straw square, and it tilts and its right angles change. That’s why bridges and roof frames use lots of triangles.
⭕ Part 4: Circles
- Centre: the middle point
- Radius: a line from the centre to the edge
- Diameter: a line from edge to edge, passing through the centre
Diameter = 2 × Radius
A roti with a radius of 8 cm has a diameter of 16 cm. Fold a paper circle in half many times: every fold line is a diameter, and they all cross at the centre!
❌ Common Mistakes to Avoid
Calling a cube a “square”
✅ A square is flat (2D). A cube is solid (3D).
✅ A square is flat (2D). A cube is solid (3D).
Counting a sphere’s edges
✅ A sphere has no edges or corners.
✅ A sphere has no edges or corners.
Thinking a diameter can go anywhere
✅ It must pass through the centre.
✅ It must pass through the centre.
Judging angles by the length of the lines
✅ Only the opening matters.
✅ Only the opening matters.
✏️ Practice Time
Try these on your own first, then check your answer below each question.
Q1. Name the shape: a matchbox, a football, a tent.
✅ AnswerCuboid, sphere, triangular prism
Q2. How many edges does a cuboid have?
✅ Answer12
Q3. A circle’s radius is 6 cm. What is its diameter?
✅ Answer12 cm
Q4. Is the angle between clock hands at 3 o’clock right, acute, or obtuse?
✅ AnswerRight angle
Q5. Which shape has 1 flat face, 1 curved face, and 1 tip?
✅ AnswerCone
📘 NCERT Textbook Activity Help
Hints and answers for the activities in the textbook, page by page. Try each one yourself before looking at the answer!
Pages 1–2 · Models of buildingsIndia Gate and Qutub Minar
✅ AnswerUse cuboids for the base and pillars and a cuboid for the top of India Gate. For the Qutub Minar, use cylinders (or cones cut at the top) stacked one above another. It has 5 storeys, so use about 5 pieces, each smaller than the one below. All bricks are cuboids (rectangular faces).
Page 3 · Prisms and pyramidsCommon faces
✅ AnswerAll prisms have rectangular side faces. Their ends are triangles, squares, or hexagons (2 each). All pyramids have triangular side faces that meet at one point. Their base can be a triangle, square, or pentagon. Yes, a cube is a prism (a square prism). A prism has 2 matching ends and rectangular sides. A pyramid has 1 base and triangular sides meeting at a point.
Page 4 · Faces, corners, and edgesTable and sorting
✅ Answer
F + V − E is always 2!
By flat faces: 1 = cone · 2 = cylinder · 4 = triangular pyramid · 5 = square pyramid, triangular prism · 6 = cube, cuboid · 8 = hexagonal prism. A shape with only 3 flat faces is not possible.
By edges: 6 = triangular pyramid · 8 = square pyramid · 9 = triangular prism · 12 = cube, cuboid
Page 5 · Let Us Observe| Shape | F | V | E | F + V − E |
|---|---|---|---|---|
| Cube | 6 | 8 | 12 | 2 |
| Cuboid | 6 | 8 | 12 | 2 |
| Triangular pyramid | 4 | 4 | 6 | 2 |
| Square pyramid | 5 | 5 | 8 | 2 |
| Triangular prism | 5 | 6 | 9 | 2 |
By flat faces: 1 = cone · 2 = cylinder · 4 = triangular pyramid · 5 = square pyramid, triangular prism · 6 = cube, cuboid · 8 = hexagonal prism. A shape with only 3 flat faces is not possible.
By edges: 6 = triangular pyramid · 8 = square pyramid · 9 = triangular prism · 12 = cube, cuboid
Dice and cube views
✅ Answer
Opposite faces of a die always add up to 7: (a) 2 ↔ 5 (b) 3 ↔ 4 (c) 4 ↔ 3
Faces touching 1: 2, 3, 4, 5. No common edge with 1: 6
Cube views: opposite of red = purple (red touches orange, green, blue, and yellow). Opposite of yellow = orange (work it out by turning a real box coloured the same way).
Border shapes: rectangular faces → boxes, erasers, dice · triangular faces → cheese piece, pyramid, cone cap (curved) · curved faces → balls, bottles, cap · no corners → balls (spheres), and a cylinder has no corners either · same opposite faces → cubes, cuboids, cylinders
Pages 6–7 · Sorting and cube towersFaces touching 1: 2, 3, 4, 5. No common edge with 1: 6
Cube views: opposite of red = purple (red touches orange, green, blue, and yellow). Opposite of yellow = orange (work it out by turning a real box coloured the same way).
Border shapes: rectangular faces → boxes, erasers, dice · triangular faces → cheese piece, pyramid, cone cap (curved) · curved faces → balls, bottles, cap · no corners → balls (spheres), and a cylinder has no corners either · same opposite faces → cubes, cuboids, cylinders
Venn diagrams
✅ AnswerAll faces look the same: cube, sphere, triangular pyramid (if its faces are equal). Faces not the same: cuboid, cylinder, cone, prisms. Triangular prism and rectangular pyramid go in the overlap, since they have both triangular and rectangular faces. Curved faces: sphere, cylinder, cone. Flat faces: cube, cuboid, prisms, pyramids. The cylinder and cone have both. For cube towers, count layer by layer, and remember the hidden cubes at the back and bottom.
Page 8 · Match descriptionsName the shape
✅ Answer(a) Square pyramid (b) Cone (c) Sphere (d) Cylinder (e) Triangular prism (f) Cube or cuboid. Each is different in the number and shape of its faces, edges, and corners.
Page 9 · NetsMatch the nets
✅ AnswerQ3: (1) triangles → (b) triangular pyramid · (2) rectangle + 2 circles → (d) cylinder · (3) 6 rectangles → (a) cuboid · (4) rectangles + 2 triangles → (c) triangular prism
Q4: B (2 circles + rectangle) makes the cylinder, and C (triangles) makes the pyramid. A and D make the boxes. Match the size of their rectangles to the yellow cube and the flat pink box.
Q5: 1 pentagon + 5 triangles → a pentagonal pyramid (the pyramid with a 5-sided base)
Pages 10–13 · AnglesQ4: B (2 circles + rectangle) makes the cylinder, and C (triangles) makes the pyramid. A and D make the boxes. Match the size of their rectangles to the yellow cube and the flat pink box.
Q5: 1 pentagon + 5 triangles → a pentagonal pyramid (the pyramid with a 5-sided base)
Finding angles
✅ AnswerCount every corner where two lines meet (the boat usually has about 7–8). Angles in the classroom: book corners, window frames, a door opening, scissors, a clock. Right angles: book, window, blackboard, table top, door. Acute: tip of a set square, a pencil tip, partly open scissors. Obtuse: an open door, a laptop screen leaning back. Letters: L, T, E, F, H have right angles, and V, A, N, M, W have acute angles.
Pages 14–16 · Shapes with strawsRigid and changing shapes
✅ AnswerTriangle: No, its shape does not change (it’s rigid). A triangle has acute and/or right/obtuse angles. Rectangle: it has 4 right angles, and Yes, it changes when pushed. It becomes a parallelogram with 2 acute and 2 obtuse angles, so they are no longer right angles. The same happens to a square (it becomes a rhombus). A regular pentagon’s angles are obtuse (not right angles), and yes, it changes when pushed. For a circle made with straws, the straws are equal in length. Unequal straws won’t give a round shape. Dots at an equal distance from A give a circle.
Pages 17–18 · Amazing circlesRadius and diameter
✅ AnswerAll the creases are equal. They are diameters and all pass through the centre. The diameter is double the radius.
Page 19 · Wheels and puzzlesWheels and puzzling shapes
✅ AnswerAll wheels look like circles. Longest radius and diameter: B (the biggest wheel). Shortest: D (the smallest).
Hidden shapes: circle, cylinder, cone, triangles, squares, and rectangles.
Q2: Draw one line straight down from the middle of the long slanting side, and one straight across to the upright side. You get a square in the corner and 2 triangles.
Q3: Draw lines from one corner to the two far corners’ midpoints, or from one top corner to the bottom corners. Any 2 lines from one corner that make 3 triangles work.
Pages 21–23 · Let Us TryHidden shapes: circle, cylinder, cone, triangles, squares, and rectangles.
Q2: Draw one line straight down from the middle of the long slanting side, and one straight across to the upright side. You get a square in the corner and 2 triangles.
Q3: Draw lines from one corner to the two far corners’ midpoints, or from one top corner to the bottom corners. Any 2 lines from one corner that make 3 triangles work.
Webs, matchsticks, and angles
✅ Answer
Squiggly: 10 triangles (4 small ones in the crossed rectangle, 4 bigger half-rectangle ones, and the top and bottom triangles). Yes, she can start and end at A without repeating a wall, because every corner has an even number of walls.
Wiggly: count the rectangles in rows and columns, plus the bigger rectangles made by joining them, and the small one on top. He can go from A to B without repeating a wall only if A and B are the only corners with an odd number of walls. Check this in your book.
Q2: Make a diamond (rhombus) with 4 sticks, and put the 5th stick across the middle.
Q5: (a) 12 straws, 8 balls → cube/cuboid (b) 9, 6 → triangular prism (c) 15, 10 → pentagonal prism (d) 10, 6 → pentagonal pyramid
Q6: The number of angles = the number of sides.
Q8: Only the rectangle and the square have 4 right angles. The others have 0 or 1.
Q9: 4 right angles → the squares and rectangles (like 6, 12, 14, and the tilted square 4). For the others, test each corner with your right angle checker.
Wiggly: count the rectangles in rows and columns, plus the bigger rectangles made by joining them, and the small one on top. He can go from A to B without repeating a wall only if A and B are the only corners with an odd number of walls. Check this in your book.
Q2: Make a diamond (rhombus) with 4 sticks, and put the 5th stick across the middle.
Q5: (a) 12 straws, 8 balls → cube/cuboid (b) 9, 6 → triangular prism (c) 15, 10 → pentagonal prism (d) 10, 6 → pentagonal pyramid
Q6: The number of angles = the number of sides.
Q8: Only the rectangle and the square have 4 right angles. The others have 0 or 1.
Q9: 4 right angles → the squares and rectangles (like 6, 12, 14, and the tilted square 4). For the others, test each corner with your right angle checker.
👨👩👧 Tips for Parents
- Collect empty boxes and packets. Open them flat to see their nets.
- Go on a shape hunt in the kitchen: cylinder (glass), sphere (orange), cuboid (tea box).
- Make a right angle checker from paper and test corners around the house.