NCERT Solutions Class 9 Maths Chapter 11 teaches you how to calculate surface areas and volumes of 3D shapes like cubes, cuboids, cylinders, cones, spheres, and hemispheres. You’ll learn to apply formulas for curved surface area, total surface area, and volume to solve real-world problems involving packaging, construction, and capacity. Each solution includes detailed steps, diagram explanations, and formula derivations to help you visualize concepts and avoid calculation errors in exams.
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All exercises with step-by-step solutions | Updated 2025-26 | Free Download
Download PDF (Free)NCERT Solutions Class 9 Maths Chapter 11 Surface Areas and Volumes – Complete Guide
NCERT Class 9 Chapter 11 – Surface Areas and Volumes introduces you to the fascinating world of three-dimensional geometry, a topic that carries significant weightage of 7 marks in your CBSE board examination. This chapter builds upon your understanding of two-dimensional shapes and extends it to solid figures that you encounter in everyday life, from water tanks and ice cream cones to footballs and dice.
📊 CBSE Class 9 Maths Chapter 11 – Exam Weightage & Marking Scheme
| CBSE Board Marks | 7 Marks |
| Unit Name | Mensuration |
| Difficulty Level | Medium |
| Importance | High |
| Exam Types | CBSE Board, State Boards |
| Typical Questions | 2-3 questions |
You’ll explore the surface areas and volumes of fundamental 3D shapes including cubes, cuboids, right circular cylinders, right circular cones, spheres, and hemispheres. You will learn to distinguish between lateral surface area (curved surface area) and total surface area, understanding when to apply each concept. The chapter provides clear derivations of formulas and numerous solved examples that demonstrate how to calculate dimensions, surface areas, and volumes efficiently.
This chapter is highly important for CBSE exams as questions regularly appear in various formats – from 2-mark MCQs testing formula application to 3-mark problems involving conversions between units, and even 4-mark questions requiring you to combine multiple concepts. You’ll also encounter practical problems like finding the cost of painting a cylindrical tank or determining how many spherical balls can be made from a given amount of material.
Quick Facts – Class 9 Chapter 11
| 📖 Chapter Number | Chapter 11 |
| 📚 Chapter Name | Surface Areas and Volumes |
| ✏️ Total Exercises | 4 Exercises |
| ❓ Total Questions | 36 Questions |
| 📅 Updated For | CBSE Session 2025-26 |
Mastering Surface Areas and Volumes not only strengthens your problem-solving abilities but also prepares you for advanced topics in Class 10 and competitive examinations. The concepts you learn here have direct applications in architecture, engineering, packaging industries, and everyday situations. With consistent practice using NCERT solutions and understanding the underlying principles, you’ll confidently tackle any question from this chapter and secure full marks in your CBSE board examination.
NCERT Solutions Class 9 Maths Chapter 11 – All Exercises PDF Download
Download exercise-wise NCERT Solutions PDFs for offline study
| Exercise No. | Topics Covered | Download PDF |
|---|---|---|
| EXERCISE 11.1 | Complete step-by-step solutions for 8 questions | 📥 Download PDF |
| EXERCISE 11.2 | Complete step-by-step solutions for 9 questions | 📥 Download PDF |
| EXERCISE 11.3 | Complete step-by-step solutions for 9 questions | 📥 Download PDF |
| EXERCISE 11.4 | Complete step-by-step solutions for 10 questions | 📥 Download PDF |
Surface Areas and Volumes – Key Formulas & Concepts
Quick reference for CBSE exams
| Formula | Description | When to Use |
|---|---|---|
| Surface Area of Cube \(6a^2\) | Total surface area of a cube, where ‘a’ is the side length Note: Make sure ‘a’ is in the correct units (e.g., cm, m). All sides of a cube are equal. | When you need to find the total area covering the outside of a cube-shaped object. |
| Lateral Surface Area of Cube \(4a^2\) | Area of the four side faces of a cube, excluding the top and bottom faces. Note: Sometimes called ‘curved surface area’. Remember to exclude top and bottom. | When you need to find the area of the sides only, like painting the walls of a cubical room. |
| Surface Area of Cuboid \(2(lb + bh + hl)\) | Total surface area of a cuboid, where ‘l’ is length, ‘b’ is breadth, and ‘h’ is height. Note: Make sure l, b, and h are in the same units. Remember to multiply by 2. | When you need the total area of all faces of a rectangular box. |
| Lateral Surface Area of Cuboid \(2h(l + b)\) | Area of the four side faces of a cuboid, excluding the top and bottom faces. Note: Sometimes called ‘curved surface area’. Remember to exclude top and bottom. | When you need to find the area of the sides of a rectangular room, like painting the walls. |
| Surface Area of Cylinder \(2\pi r(r + h)\) | Total surface area of a closed cylinder, where ‘r’ is the radius and ‘h’ is the height. Note: Use \(\pi = \frac{22}{7}\) unless the question specifies otherwise. Make sure r and h are in the same units. | When you need the total area of a cylindrical object, including the top and bottom circles. |
| Curved Surface Area of Cylinder \(2\pi rh\) | Area of the curved surface of a cylinder, excluding the top and bottom circles. Note: This is the area of just the curved part, not the top and bottom. | When you need the area of the curved surface of a cylindrical object, like wrapping paper around a can. |
| Surface Area of Cone \(\pi r(l + r)\) | Total surface area of a cone, where ‘r’ is the radius and ‘l’ is the slant height. Note: Remember ‘l’ is the slant height, not the height. If height is given, find slant height using Pythagorean theorem. | When you need the total area of a cone-shaped object, including the circular base. |
| Curved Surface Area of Cone \(\pi rl\) | Area of the curved surface of a cone, excluding the circular base. Note: Only the curved part, not the base. | When you need the area of the curved part of a cone, like the paper used to make an ice cream cone. |
| Slant Height of Cone \(l = \sqrt{r^2 + h^2}\) | Calculates the slant height ‘l’ of a cone, given the radius ‘r’ and height ‘h’. Note: This is based on the Pythagorean theorem. Make sure r and h are in the same units. | When you need to find the slant height to use in surface area formulas, but you only have the radius and height. |
| Surface Area of Sphere \(4\pi r^2\) | Total surface area of a sphere, where ‘r’ is the radius. Note: Remember that a sphere has no curved surface area separate from its total surface area. | When you need the area covering the entire outside of a ball. |
| Surface Area of Hemisphere \(3\pi r^2\) | Total surface area of a solid hemisphere (including the circular base). Note: Includes the curved surface and the flat circular base. | When you need the total area of a half-sphere, like a bowl. |
| Curved Surface Area of Hemisphere \(2\pi r^2\) | Area of the curved surface of a hemisphere, excluding the circular base. Note: Does NOT include the circular base. | When you need the area of only the curved part of a hemisphere. |
| Volume of Cube \(a^3\) | The amount of space inside a cube with side length ‘a’. Note: Units will be cubed (e.g., cm³, m³). | Calculating how much a cube can hold (e.g., water, sand). |
| Volume of Cuboid \(lwh\) | The amount of space inside a cuboid with length ‘l’, width ‘w’, and height ‘h’. Note: Units will be cubed (e.g., cm³, m³). | Calculating how much a rectangular box can hold. |
| Volume of Cylinder \(\pi r^2 h\) | The amount of space inside a cylinder with radius ‘r’ and height ‘h’. Note: Units will be cubed (e.g., cm³, m³). | Calculating how much a cylindrical container can hold. |
| Volume of Cone \(\frac{1}{3}\pi r^2 h\) | The amount of space inside a cone with radius ‘r’ and height ‘h’. Note: Units will be cubed (e.g., cm³, m³). Remember the 1/3 factor. | Calculating how much an ice cream cone can hold. |
| Volume of Sphere \(\frac{4}{3}\pi r^3\) | The amount of space inside a sphere with radius ‘r’. Note: Units will be cubed (e.g., cm³, m³). | Calculating how much a ball can hold (if it were hollow). |
| Volume of Hemisphere \(\frac{2}{3}\pi r^3\) | The amount of space inside a hemisphere with radius ‘r’. Note: Units will be cubed (e.g., cm³, m³). | Calculating how much a hemispherical bowl can hold. |
Frequently Asked Questions – NCERT Class 9 Maths Chapter 11
📚 Related Study Materials – Class 9 Maths Resources
| Resource | Access |
|---|---|
| NCERT Class 9 Mathematics Textbook | Download Book |
| NCERT Class 9 Science Solutions | View Solutions |
| RD Sharma Class 9 (Updated 2025-26) | View Solutions |
| NCERT Class 9 English (Beehive) | Download Book |