Boxes and Sketches — Class 5 Mathematics (CBSE)
Based on the NCERT Math Magic Grade 5 textbook. Understand 3D shapes through nets and sketches, then solve the practice set without looking at the answers.
1. Why this chapter matters
We live in a three-dimensional world. Boxes, balls, bottles, buildings — everything around us has length, breadth, and height. This chapter helps students visualise 3D objects in 2D drawings. They learn about nets (flat patterns that fold into 3D shapes), oblique sketches, isometric sketches, and deep drawings. These skills are fundamental for geometry, architecture, design, and engineering.
2. 3D shapes
Three-dimensional shapes have length, breadth, and height. Unlike flat (2D) shapes, they also have volume.
Common 3D shapes
| Shape | Faces | Edges | Vertices | Real-life example |
|---|---|---|---|---|
| Cube | 6 (all squares) | 12 | 8 | Dice, Rubik's cube |
| Cuboid | 6 (all rectangles) | 12 | 8 | Book, brick, shoebox |
| Sphere | 1 curved | 0 | 0 | Ball, globe |
| Cylinder | 2 flat + 1 curved | 2 | 0 | Can, pipe, roller |
| Cone | 1 flat + 1 curved | 1 | 1 | Ice-cream cone, birthday hat |
| Pyramid | 5 (1 square + 4 triangles) | 8 | 5 | Egyptian pyramid |
Faces, edges, and vertices
- Face: A flat surface of a 3D shape.
- Edge: Where two faces meet.
- Vertex: Where three or more edges meet (plural: vertices).
For a cube: 6 faces, 12 edges, 8 vertices. For a cuboid: 6 faces, 12 edges, 8 vertices.
3. Nets of cubes and cuboids
A net is a flat pattern that can be folded to form a 3D shape. It shows all the faces of the shape in two dimensions.
Net of a cube
A cube has 6 square faces. Its net is made of 6 connected squares arranged so that they fold into a cube.
There are 11 different nets for a cube. The most common ones look like a cross (T-shape):
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Net of a cuboid
A cuboid's net has 6 rectangular faces — 3 pairs of equal rectangles.
Example net of a cuboid (2 x 3 x 4 cm):
- Top and bottom: 2 rectangles of 2 cm x 3 cm
- Front and back: 2 rectangles of 2 cm x 4 cm
- Left and right sides: 2 rectangles of 3 cm x 4 cm
How to check if a net works
- Visualise folding along the edges.
- Each face must connect to its neighbour.
- No face should overlap with another when folded.
- When folded, all edges should meet exactly.
4. Oblique sketches
An oblique sketch is a quick way to draw a 3D shape on paper. It shows the front face as a normal 2D shape and the depth as slanted lines.
Drawing an oblique sketch of a cuboid
- Draw the front face as a rectangle (true shape).
- From each corner, draw a slanted line to show depth (usually at 45° angle).
- The slanted lines should all be the same length (shorter than actual depth to create perspective).
- Connect the ends of the slanted lines to form the back face.
- Use dashed lines for edges that would be hidden from view.
Characteristics: The front face looks accurate, but the shape looks slightly distorted because parallel lines in depth are shown as parallel (not converging).
5. Isometric sketches
An isometric sketch shows a 3D shape more realistically. It uses isometric dot paper where dots are arranged in a grid of equilateral triangles.
Drawing an isometric sketch of a cube
- On isometric dot paper, draw a vertical line for one edge.
- From the top and bottom of this line, draw lines at 30° to the horizontal to show width and depth.
- Complete the shape by connecting parallel lines.
- All edges that are parallel in reality remain parallel in the sketch.
Characteristics: Isometric sketches look more realistic than oblique sketches. All three dimensions (length, breadth, height) are shown with correct proportions.
| Feature | Oblique sketch | Isometric sketch |
|---|---|---|
| Front face | True shape | Shown at angle |
| Depth lines | 45° angle | 30° angle |
| Realism | Less realistic | More realistic |
| Paper needed | Plain paper | Isometric dot paper |
| Ease of drawing | Easier | Requires practice |
6. Deep drawings
A deep drawing shows how objects look from different viewpoints — top view, front view, and side view.
Views of a brick
| View | What you see |
|---|---|
| Top view | A rectangle |
| Front view | A rectangle (different proportions) |
| Side view | A smaller rectangle |
Matching views to objects
Activity: Place a cuboid on your desk. Walk around it. Draw what you see from the front, side, and top. Notice how the shape changes.
Stacking boxes
When boxes are stacked, the views become more complex.
- Top view: Shows the outline of the arrangement from above.
- Front view: Shows the height and width arrangement.
- Side view: Shows the depth and height arrangement.
7. Activity corner
Activity 1: Collect 5 different boxes (medicine box, toothpaste box, matchbox, etc.). Open each one carefully along its edges to create a net. Trace the net on paper and label the faces.
Activity 2: Use isometric dot paper to draw a cube, a cuboid, and a simple house shape.
Activity 3: Arrange 4 cubes in an L-shape. Draw the top view, front view, and side view of your arrangement.
8. Common mistakes
- Mistake: Drawing a net that cannot fold into a closed shape Fix: Check that every face connects to at least one neighbour and that no more than 4 faces meet at any point.
- Mistake: Confusing oblique with isometric sketches Fix: Oblique = front face is flat, depth at 45°. Isometric = all edges at 30°, uses dot paper.
- Mistake: Forgetting to show hidden edges with dashed lines Fix: In sketches, use dashed lines for edges that would be hidden behind the front face.
9. Key facts
- A cube has 6 faces, 12 edges, 8 vertices.
- A net is a flat pattern that folds into a 3D shape.
- There are 11 different nets for a cube.
- Oblique sketches show depth at 45°.
- Isometric sketches use dot paper with 30° angles.
- Top view, front view, and side view show a shape from different angles.
- Hidden edges are shown with dashed lines.
10. Self-test
- How many faces does a cube have? What shape are each of them?
- What is a net of a 3D shape?
- Draw the top view of a cylinder.
- How many edges does a cuboid have?
- What is the difference between an oblique sketch and an isometric sketch?
11. Answer key
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How many faces does a cube have? What shape are each of them? Answer: A cube has 6 faces. Each face is a square.
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What is a net of a 3D shape? Answer: A net is a flat pattern made of connected faces that can be folded to form a 3D shape.
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Draw the top view of a cylinder. Answer: A circle (or a rectangle with rounded ends in a simplified drawing).
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How many edges does a cuboid have? Answer: 12 edges.
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What is the difference between an oblique sketch and an isometric sketch? Answer: In an oblique sketch, the front face is drawn as a true shape and depth lines are at 45°. In an isometric sketch, all dimensions are shown at 30° on isometric dot paper, giving a more realistic appearance.
12. Quick revision
- 3D shapes have length, breadth, and height.
- Nets fold into 3D shapes — practise visualising the fold.
- Oblique sketches are quick; isometric sketches are more realistic.
- Draw top, front, and side views to understand shape from all angles.
- Collect boxes to see their nets in real life.
- Use isometric dot paper to practise 3D drawing.
