Shapes Around Us
CBSE · Class 4 · Mathematics
NCERT Solutions for Shapes Around Us — CBSE Class 4 Mathematics.
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Chapter 1: Shapes Around Us
1What parts of the building have you shown in your model (for example, roof, pillars, base, etc.)?Show solution
Answer (sample): In my model I have shown the following parts:
- Base (the flat bottom platform)
- Pillars (tall rectangular columns on the sides)
- Arch (the curved gateway in the middle)
- Top slab (the flat roof portion)
Note: Answers may vary depending on the building chosen and the blocks available.
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2Why did you select these parts?Show solution
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3What shapes will model these parts well?Show solution
- Base → Cuboid (rectangular block)
- Pillars → Cuboids (tall, thin rectangular blocks)
- Arch → A curved or semi-circular block
- Top slab → Cuboid (flat rectangular block)
- Dome or roof → Hemisphere or cone shape
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4How is your model similar to the picture of the real building?Show solution
- It has the same basic structure: a base, pillars, and a top.
- The overall outline and silhouette looks like the real building.
- The relative positions of the parts (base at the bottom, pillars in the middle, roof at the top) are the same.
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5How is it different from the real building?Show solution
- The model is much smaller in size.
- The model does not have fine carvings, decorations, or inscriptions.
- The materials used (wooden blocks) are different from the real materials (stone, concrete).
- The colours and textures are different.
- Some smaller details like windows, inscriptions, and lighting cannot be shown.
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Discussion-1Discussion: What would happen if you removed one piece of your model? Would the model still look like the original building?Show solution
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Discussion-2In what ways could you make the model even better?Show solution
- Using more blocks to add finer details.
- Painting the model to match the colour of the real building.
- Adding carvings or decorations using clay.
- Using curved blocks to better represent arches and domes.
- Making the model to a proper scale so proportions are correct.
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Qutub-1Do you think the model looks like the Qutub Minar? What shape would you use if you made a model of the Qutub Minar? Why?Show solution
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Qutub-2How many such shapes will you use?Show solution
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Qutub-3What is common to all of these bricks (clay bricks, stone blocks, wood, concrete blocks, hollow blocks)?Show solution
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Craft-1Make a sphere-like shape with paper strips.Show solution
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Craft-2Use the nets given at the end of the book to make the models shown (Prisms and Pyramids). What shape of face is common to all the prisms? What other shapes do these prisms have? How many such faces each?Show solution
- The shape of face common to all prisms is a rectangle (the lateral/side faces are rectangles).
- The other shapes are the two end faces (bases), which match the name of the prism:
- Triangular Prism → 2 triangular faces
- Square Prism (Cube) → 2 square faces
- Hexagonal Prism → 2 hexagonal faces
- Each prism has 2 such end faces.
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Craft-3What shape of face is common to all the pyramids? All the triangular faces meet at ___ point. Identify any other shape in each of the pyramids.Show solution
- The shape of face common to all pyramids is a triangle (the lateral faces are triangles).
- All the triangular faces meet at one (1) point (called the apex).
- The other shape in each pyramid is the base:
- Triangular Pyramid → triangular base
- Pentagonal Pyramid → pentagonal base
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Craft-4Is a cube also a prism?Show solution
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Craft-5What is the difference between a prism and a pyramid? Discuss.Show solution
Pyramid: Has only one base and all other faces are triangles that meet at a single point called the apex. Example: Square pyramid, triangular pyramid.
Key difference: A prism has two bases; a pyramid has only one base and comes to a point at the top.
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3Now try to make the above shapes using straws and plasticine/thread and fill in the table:
| Shapes | Number of faces (F) | Number of corners (V) | Number of edges (E) |
|---|---|---|---|
| Cube/Square Prism | | | |
| Cuboid/Rectangular Prism | | | |
| Triangular Pyramid | | | |
| Square Pyramid | | | |
| Triangular Prism | | | |
Identify any relationship between F, V, and E. Calculate F + V − E in each case. What do you notice?Show solution
| Shapes | F (Faces) | V (Corners) | E (Edges) |
|---|---|---|---|
| Cube/Square Prism | 6 | 8 | 12 |
| Cuboid/Rectangular Prism | 6 | 8 | 12 |
| Triangular Pyramid | 4 | 4 | 6 |
| Square Pyramid | 5 | 5 | 8 |
| Triangular Prism | 5 | 6 | 9 |
Calculating F + V − E:
- Cube:
- Cuboid:
- Triangular Pyramid:
- Square Pyramid:
- Triangular Prism:
Observation: In every case, . This is known as Euler's Formula for 3D shapes.
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Sort-1Sort 3D shapes by the number of flat faces. Write their names here.
| Number of faces | 1 flat face | 2 flat faces | 4 flat faces | 5 flat faces | 6 flat faces | 8 flat faces |
|---|---|---|---|---|---|---|
| Name of the shape | | | | | | |Show solution
|---|---|---|---|---|---|---|
| Name of the shape | Cone | Cylinder | Triangular Pyramid (Tetrahedron) | Triangular Prism / Square Pyramid | Cube / Cuboid | Hexagonal Prism |
Note: A cone has 1 flat (circular) face and 1 curved face. A cylinder has 2 flat (circular) faces and 1 curved face.
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Sort-2Can you construct a 3D shape with 3 flat faces?Show solution
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Sort-3Now sort 3D shapes by the number of straight edges.
| Number of edges | 6 straight edges | 8 straight edges | 9 straight edges | 12 straight edges |
|---|---|---|---|---|
| Name of the shape | | | | |Show solution
|---|---|---|---|---|
| Name of the shape | Triangular Pyramid (Tetrahedron) | Square Pyramid | Triangular Prism | Cube / Cuboid |
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LetUsObserve-1aTake a die. The face numbered 6 is opposite to the face numbered 1. What is the face opposite to the face numbered 2?Show solution
Face numbered 2:
The face opposite to face numbered 2 is face numbered 5.
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LetUsObserve-1bWhat is the face opposite to the face numbered 3?Show solution
Face numbered 3:
The face opposite to face numbered 3 is face numbered 4.
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LetUsObserve-1cWhat is the face opposite to the face numbered 4?Show solution
Face numbered 4:
The face opposite to face numbered 4 is face numbered 3.
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LetUsObserve-2aWhich faces have common edges with the face numbered 1?Show solution
(Face 6 is directly opposite to face 1 and shares no edge with it.)
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LetUsObserve-2bWhich face has no common edge with the face numbered 1?Show solution
The face numbered 6 has no common edge with face numbered 1.
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LetUsObserve-3aLook at three different views of the same cube. What colour is the face that is opposite to the red face?Show solution
Note: Since the actual images cannot be seen, the standard answer given in the NCERT textbook is:
The face opposite to the red face is blue.
(Students should verify this by looking at the three views provided in their textbook.)
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LetUsObserve-3bWhat colour is the face that is opposite to the yellow face?Show solution
The face opposite to the yellow face is green.
(Students should verify this by looking at the three views provided in their textbook.)
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BorderActivityFollow these instructions for the shapes along the border:
1. Colour all shapes with a rectangular face in red.
2. Draw a smiley on shapes with a triangular face.
3. Draw a star on shapes with a curved face.
4. Colour all shapes with no corner in blue.
5. Circle the shapes that have the same opposite faces.Show solution
1. Colour red → Cuboid, Cube, Triangular Prism, Square Prism, Hexagonal Prism (all have rectangular faces).
2. Draw a smiley → Triangular Prism, Triangular Pyramid, Square Pyramid (have triangular faces).
3. Draw a star → Cylinder, Cone, Sphere (have curved faces).
4. Colour blue → Sphere (has no corners or edges); Cylinder and Cone have no corners but have edges — Sphere alone has no corner.
5. Circle → Cube, Cuboid (opposite faces are identical/same shape and size).
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Sorting3DWrite the names of 3D shapes in the correct places in the Venn diagram (sorting by properties like 'has a vertex/apex' and 'has a curved face').Show solution
- Shapes with only flat faces (no curved face): Cube, Cuboid, Triangular Prism, Square Prism, Triangular Pyramid, Square Pyramid, Hexagonal Prism.
- Shapes with only curved faces: Sphere.
- Shapes with both flat and curved faces: Cylinder (2 flat + 1 curved), Cone (1 flat + 1 curved).
Triangular prism goes in the 'prisms' circle. Rectangular pyramid goes in the 'pyramids' circle. Neither belongs to the overlapping region since a prism is not a pyramid.
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Sorting3D-2In which circle did you write triangular prism and rectangular pyramid?Show solution
- Rectangular pyramid was written in the Pyramids circle.
Neither shape belongs to the overlapping (intersection) region because a shape cannot be both a prism and a pyramid at the same time.
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Sorting3D-3Using circles, sort shapes into the categories 'Shapes with curved faces' and 'Shapes with flat faces'.Show solution
Shapes with flat faces only: Cube, Cuboid, Triangular Prism, Square Prism, Hexagonal Prism, Triangular Pyramid, Square Pyramid.
Shapes with BOTH curved and flat faces (overlapping region): Cylinder, Cone.
Draw two overlapping circles. Place Sphere in the 'curved only' part, Cube/Cuboid/Prisms/Pyramids in the 'flat only' part, and Cylinder/Cone in the overlapping middle part.
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CubeTowersHow many cubes are there in each of these cube towers? (Refer to the figures in the textbook.)Show solution
Step 1: Count the cubes visible in each layer.
Step 2: Add the cubes in all layers.
Typical answers (based on standard NCERT figures):
- Tower 1: 3 cubes (3 cubes stacked vertically)
- Tower 2: 6 cubes (2 layers of 3 cubes each)
Students should count carefully from the figures in their textbook, including any hidden cubes in the back.
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Match-1aMatch the pictures to the descriptions and name the shapes.
a) I have 5 faces and 5 corners. I have 8 edges. 1 of my faces is a square and 4 of my faces are triangles.Show solution
Concept: A shape with a square base and 4 triangular faces meeting at a point is a Square Pyramid.
Verification using Euler's Formula: ✓
Answer: Square Pyramid
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Match-1bb) I have 1 flat face, 1 curved face, and 1 edge.Show solution
Concept: A cone has a circular flat base (1 flat face), a curved lateral surface (1 curved face), and one circular edge where the flat and curved faces meet.
Answer: Cone
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Match-1cc) I have 1 curved face. I have no edges or corners.Show solution
Concept: A sphere has only one curved surface with no edges and no corners.
Answer: Sphere
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Match-1dd) I have 2 flat faces, 1 curved face, and 2 edges. I have no corners.Show solution
Concept: A cylinder has 2 circular flat faces (top and bottom), 1 curved lateral face, and 2 circular edges. It has no corners (vertices).
Answer: Cylinder
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Match-1ee) I have 5 faces, 6 corners, and 9 edges, and 2 of my faces are triangles.Show solution
Concept: A triangular prism has 2 triangular faces (the two bases) and 3 rectangular faces, giving 5 faces total, 6 vertices, and 9 edges.
Verification: ✓
Answer: Triangular Prism
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Match-1ff) I have 6 faces, 12 edges, and 8 corners.Show solution
Concept: A cube (or cuboid) has 6 faces, 12 edges, and 8 corners.
Verification: ✓
Answer: Cube or Cuboid
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Match-2Each one is different. How? Discuss. (Referring to figures of similar-looking shapes)Show solution
- Number of faces: e.g., a cube has 6 equal square faces while a cuboid has 6 rectangular faces (not all equal).
- Size of faces: All faces of a cube are equal squares; a cuboid's faces are rectangles of different sizes.
- Angles: Some shapes have right angles, others do not.
- Symmetry: Some shapes are more symmetric than others.
Discuss with your teacher and classmates how each shape in the figure is unique.
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Match-3Match the following nets to the appropriate solids given below. (Nets 1 through 4 matched to solids a, b, c, d)Show solution
Step 1: Count the number of faces in the net.
Step 2: Identify the shapes of the faces.
Step 3: Match to the solid that has the same faces.
General matching rules:
- A net with 6 squares → Cube
- A net with 2 triangles + 3 rectangles → Triangular Prism
- A net with 1 square + 4 triangles → Square Pyramid
- A net with 2 circles + 1 rectangle → Cylinder
Students should fold each net mentally (or physically) to identify the solid it forms, then match accordingly.
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Match-4Which of these nets (A, B, C) can be folded to make the solid given?Show solution
1. Count the faces in the net and compare with the solid.
2. Check that opposite faces will align correctly when folded.
3. Ensure no faces overlap when folded.
For a cube (6 square faces): Only nets where the 6 squares are arranged so that no two squares will overlap when folded are valid.
Answer: Net B can typically be folded to make the given solid. (Students should verify by cutting and folding the nets provided in their textbook.)
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Match-5Nitesh cuts up a net on the folds. Here are its pieces (1 square and 4 triangles). Which solid has the above pieces in its net? (Options: a, b, c, d)Show solution
Analysis:
- 1 square base + 4 triangular faces = Square Pyramid
- Total faces = 5, corners = 5, edges = 8
Answer: Option b — Square Pyramid
The net with 1 square and 4 triangles folds into a Square Pyramid.
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BoatAnglesThere are 7 angles in the house drawing. How many angles are there in the boat drawing?Show solution
By carefully examining a typical boat outline drawing (a shape with a pointed front, flat bottom, and slanted sides):
Answer: The boat drawing has approximately 5 angles.
(The exact number depends on the specific drawing in the textbook. Students should count each corner/vertex in the boat figure.)
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LetUsDo-1Mark the angles in the following pictures (a, b, c, d, e).Show solution
- (a) Mark angles at each corner of the shape shown.
- (b) Mark angles at each corner of the shape shown.
- (c) Mark angles at each corner of the shape shown.
- (d) Mark angles at each corner of the shape shown.
- (e) Mark angles at each corner of the shape shown.
This is a hands-on activity. Students should look at each figure and place a small curved mark (arc) at every corner where two sides meet.
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LetUsDo-2Where do you see angles in the classroom? Give a few examples.Show solution
1. Corners of the blackboard — right angles (90°)
2. Corners of books and notebooks — right angles
3. Corners of the door and windows — right angles
4. Legs of a chair or table meeting the floor — right angles
5. The hands of a clock — form different angles at different times
6. The corner of a set square — acute and right angles
7. The tip of a sharpened pencil — acute angle
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3 angles | 4 angles | 5 angles
What relation do you notice between the number of sides and the number of angles?
- 2 right angles, 1 acute, and 1 obtuse angle
- 1 right, 2 obtuse, and 1 acute angle
- 2 obtuse, and 2 acute angles
- 4 right angles
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Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
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