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JAC • Class 6 • Mathematics • Ch 14

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Three-Dimensional Shapes

Recognise cubes, cuboids, cylinders, cones and spheres; describe faces, edges and vertices.

View All Chapters JCERT Hindi Textbook

Overview Core Concepts Solved Examples Common Traps Summary Self Check Take MCQ Test

Why This Chapter Matters

Recognise cubes, cuboids, cylinders, cones and spheres; describe faces, edges and vertices.

Before You Begin (Prerequisites)

Familiarity with simple shapes and measurement

What You Will Learn (Core Objectives)

Recognise cubes, cuboids, cylinders, cones and spheres; describe faces, edges and vertices.

Chapter Roadmap & Progression

1 Syllabus and book alignment

2 Concept 1

3 Concept 2

4 Concept 3

Complete Concept Guide (100% Curriculum Coverage)

Syllabus and book alignment

JCERT 2026–27: Regular schools (Non-SOE) — Chapter 14 · Three-Dimensional Shapes. Syllabus pages 223–227. These notes follow this topic. Official syllabus. Official JCERT Hindi textbook. Some source PDFs are damaged. The supplementary reference uses different chapter numbering.

Concept 1

A solid has three dimensions: length, breadth and height. A cube has six equal square faces, twelve edges and eight vertices. A cuboid has six rectangular faces, twelve edges and eight vertices.

Concept 2

A cylinder has two flat circular faces and one curved surface. A cone has one flat circular face, one curved surface and one vertex. A sphere has one curved surface and has no edges or vertices. Curved surfaces are described separately from flat faces.

Concept 3

A dice models a cube, a brick a cuboid, a tin can a cylinder, an ice-cream cone a cone and a ball a sphere. A face is a flat surface, an edge is where faces meet, and a vertex is a corner.

Conceptual Solved Examples & Case Studies

Example 1

Compare the number of vertices in a cube and a sphere.

Step-by-Step Solution:

A cube has 8 vertices. A sphere has 0 vertices; it has no corners.

Common Misconceptions & Examiner Traps

Common Misconception

Common misconception

Scientific Reality & Correction

A circle is a plane figure; a sphere is a solid. A cylinder has a curved surface, so it is not a cuboid.

Chapter Summary & 10 Key Takeaways

Takeaway 1

A solid has three dimensions: length, breadth and height. A cube has six equal square faces, twelve edges and eight vertices. A cuboid has six rectangular faces, twelve edges and eight vertices.

Takeaway 2

Takeaway 3

A dice models a cube, a brick a cuboid, a tin can a cylinder, an ice-cream cone a cone and a ball a sphere. A face is a flat surface, an edge is where faces meet, and a vertex is a corner.

Check Your Understanding (Diagnostic Practice Questions)

Diagnostic questions testing core conceptual clarity. Answers are hidden initially — solve each problem first, then click to reveal the step-by-step verified solution.

Which solid has six equal square faces?

Reveal Answer & Explanation

Answer: A cube. It also has 12 edges and 8 vertices.
Use the definition above.

Chapter practice

CBT tests for this chapter are not published yet. Solve the self-check questions above and compare your answers.

All Class 6 Mathematics Chapters

Ch 1: Knowing Our Numbers Ch 2: Whole Numbers Ch 3: Integers Ch 4: Playing with Numbers Ch 5: Fractions Ch 6: Decimals Ch 7: Ratio and Proportion Ch 8: Algebra Ch 9: Line, Line Segment and Ray Ch 10: Pairs of Lines Ch 11: Angles Ch 12: Polygons Ch 13: Circle Ch 14: Three-Dimensional Shapes Ch 15: Symmetry Ch 16: Practical Geometry Ch 17: Perimeter and Area Ch 18: Data Handling

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