CBSE Class 10 Maths Chapter 12 – Surface Areas and Volumes (2026–27)
Master Chapter 12 – Surface Areas and Volumes with comprehensive study notes, NCERT solutions, exercise-wise solutions, MCQs, important questions, PDF downloads, and video lessons based on the latest CBSE Class 10 Mathematics (2026–27) syllabus. Learn how to calculate the surface areas and volumes of cubes, cuboids, cylinders, cones, spheres, hemispheres, and combinations of solids through easy explanations and step-by-step NCERT solutions.
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Chapter Summary
Surface Areas and Volumes introduces students to the formulas and applications of three-dimensional solids. This chapter explains how to calculate the curved surface area, total surface area, and volume of cubes, cuboids, cylinders, cones, spheres, and hemispheres. Students also learn to solve problems involving combinations and conversions of solid shapes.
By practicing NCERT exercises, solved examples, MCQs, and important questions, students strengthen their understanding of mensuration and develop the skills required to solve real-life geometry problems in the CBSE board examination.
Learning Outcomes
After completing this chapter, students will be able to:
- ✅ Understand the properties of three-dimensional solids.
- ✅ Calculate curved and total surface areas.
- ✅ Find the volumes of common solid shapes.
- ✅ Solve problems involving combinations of solids.
- ✅ Apply mensuration formulas accurately.
- ✅ Improve analytical and calculation skills.
- ✅ Solve NCERT and board-level questions confidently.
- ✅ Prepare effectively for the CBSE board examination.
Key Topics
- 🧊 Cube
- 📦 Cuboid
- 🥫 Cylinder
- 🍦 Cone
- ⚽ Sphere
- 🌐 Hemisphere
- 📏 Curved Surface Area (CSA)
- 📐 Total Surface Area (TSA)
- 📊 Volume of Solids
- 🔷 Combination of Solids
⭐ Study Resources
📝 Exercise Solutions
Step-by-step video lessons covering every concept based on the latest CBSE syllabus.
📄 Study Notes
Comprehensive notes with explanations, solved examples, and important concepts.
🧠 Mind Map
Visual chapter summary for quick revision of important concepts and formulas.
📚 Formula Sheet
Formula Sheet
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📘 NCERT Solutions
Step-by-step solutions for every NCERT textbook exercise with clear explanations.
📘 Exemplar Solutions
Detailed solutions for NCERT Exemplar questions to strengthen higher-order thinking.
📑 Important Questions
Most expected board exam questions with detailed solutions and explanations.
❓ MCQs
Chapter-wise multiple-choice questions for concept reinforcement and quick revision.
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Step-by-step video lessons covering every concept based on the latest CBSE syllabus.
📑 Competency Based Questions
Assertion & Reason and Case Study questions based on the latest CBSE pattern..
📄 PDF Notes
Additional practice questions to improve problem-solving skills and self-assessment.
📝Exercise-wise Solutions
📘 Exercise 12.1 – Surface Areas of Solids
Exercise 12.1 focuses on calculating the Curved Surface Area (CSA) and Total Surface Area (TSA) of cubes, cuboids, cylinders, cones, spheres, and hemispheres. Students learn to apply the appropriate formulas, solve practical mensuration problems, and build a strong understanding of surface area concepts through detailed NCERT solutions and step-by-step explanations.
This exercise prepares students to confidently solve both NCERT textbook questions and CBSE board examination problems related to circles and mensuration.
📘 Exercise 12.2 – Volumes of Solids
Exercise 12.2 covers the calculation of the volumes of three-dimensional solids, including cubes, cuboids, cylinders, cones, spheres, hemispheres, and combinations of solids. Students solve real-life application-based questions, conversion problems, and mensuration exercises using detailed NCERT solutions and easy-to-follow explanations, helping them prepare confidently for the CBSE board examination.
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❓ Frequently Asked Questions
1. What is Surface Areas and Volumes?
This chapter explains how to calculate the surface areas and volumes of common three-dimensional solids such as cubes, cuboids, cylinders, cones, spheres, and hemispheres.
2. How many exercises are there in Chapter 12?
Chapter 12 contains 2 exercises:
- 📘 Exercise 12.1 – Surface Areas of Solids
- 📘 Exercise 12.2 – Volumes of Solids
3. What is the difference between Curved Surface Area (CSA) and Total Surface Area (TSA)?
Curved Surface Area (CSA) is the area of only the curved surface of a solid, while Total Surface Area (TSA) includes the areas of all surfaces, including the top and bottom faces where applicable.
4. Are these notes based on the latest CBSE syllabus?
Yes. All study notes, solutions, and learning resources are prepared according to the latest CBSE Class 10 Mathematics (2026–27) syllabus.
5. Are NCERT exercise solutions available?
Yes. Step-by-step solutions for Exercise 2.1 and Exercise 2.2 are available with detailed explanations.
6. Can I download the Chapter 12 notes as a PDF?
Yes. Free PDF notes and other downloadable study resources are available on this page.
7. Are MCQs and important questions included?
Yes. This chapter includes chapter-wise MCQs, important questions, and additional practice material for exam preparation.
8.Why is Chapter 12 important for the CBSE board examination?
Chapter 12 is one of the most important and scoring chapters in Class 10 Mathematics. Questions on surface areas, volumes, and combinations of solids are frequently asked in the CBSE board examination, making this chapter essential for strengthening mensuration concepts and improving problem-solving skills.
9. Are video lessons available for this chapter?
Yes. Video lessons are provided to help students understand each concept with clear explanations and solved examples.
10. Who can use these study resources?
These resources are suitable for CBSE Class 10 students, teachers, and parents looking for reliable notes, NCERT solutions, MCQs, PDFs, and revision material.
11. Which three-dimensional solids are covered in this chapter?
This chapter covers:
- 🧊 Cube
- 📦 Cuboid
- 🥫 Cylinder
- 🍦 Cone
- ⚽ Sphere
- 🌐 Hemisphere
- 🔷 Combination of Solids
12. What is the volume of a solid?
The volume of a solid is the amount of space occupied by a three-dimensional object. It is measured in cubic units such as cm³ or m³.
13. What types of questions are asked from this chapter?
This chapter includes questions on:
- 📏 Curved Surface Area (CSA)
- 📐 Total Surface Area (TSA)
- 📊 Volume of solids
- 🔷 Combination of solids
- 📝 Real-life application and mensuration problems
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🚀Continue Learning
Keep building your mathematics skills by exploring the next chapter in the CBSE Class 10 Mathematics syllabus.
📖 Chapter 11 – Areas Related to Circles
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📖 Chapter 13 – Statistics
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