Advanced Study Material for Class 10 Mathematics: Chapter 12 Surface Area and Volume
Explore structured advanced study materials through the CBSE Class 10 Surface Areas and Volumes Important Formulas and concepts for exams. Tailored for Class 10 learners, utilizing these Mathematics resources ensures thorough preparation and strengthens foundational knowledge before final CBSE evaluations.
Practice Class 10 Mathematics Resources: Chapter 12 Surface Area and Volume
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CBSE Class 10 Surface Areas and Volumes Important Formulas and concepts for exams. Please refer to the examination notes which you can use for preparing and revising for exams. These notes will help you to revise the concepts quickly and get good marks.
This Class 10 Maths formula sheet for Surface Areas and Volumes gives the lateral or curved surface area, total surface area and volume of the cuboid, cube, right prism, cylinder, right pyramid, cone, sphere and hemisphere, along with the nomenclature of each solid. It also covers the frustum of a cone with its slant height, curved surface area, total surface area, volume and the height of the complete cone.
IMPORTANT FORMULAS AND CONCEPTS
| S. No. | Name of the solid | Figure | Lateral / Curved surface area | Total surface area | Volume | Nomenclature |
|---|---|---|---|---|---|---|
| 1 | Cuboid | [Figure: cuboid with length l, breadth b and height h marked] | 2h(l + b) | 2(lb + bh + hl) | lbh | l: length b: breadth h: height |
| 2 | Cube | [Figure: cube with each edge marked a] | 4a² | 6a² | a³ | a: side of the cube |
| 3 | Right prism | [Figure: right triangular prism] | Perimeter of base × height | Lateral surface area + 2 (area of the end surface) | Area of base × height | - |
| 4 | Regular circular Cylinder | [Figure: closed cylinder] | 2πrh | 2πr(r + h) | πr²h | r: radius of the base h: height |
| 5 | Right pyramid | [Figure: right pyramid on a square base] | \( \frac{1}{2} \) (perimeter of base) × slant height | Lateral surface area + area of the base | \( \frac{1}{3} \) × area of the base × height | - |
| 6 | Right circular cone | [Figure: cone] | πrl | πr(l + r) | \( \frac{1}{3} \) πr²h | r: radius of the base h: height l: slant height |
| 7 | Sphere | [Figure: sphere with its centre marked] | 4πr² | 4πr² | \( \frac{4}{3} \) πr³ | r: radius |
| 8 | Hemisphere | [Figure: hemisphere with its radius marked] | 2πr² | 3πr² | \( \frac{2}{3} \) πr³ | r: radius |
FRUSTUM OF A CONE
If a right circular cone is cut off by a plane parallel to its base, then the portion of the cone between the cutting plane and the base of the cone is called a frustum of a cone.
[Figure: A cone cut by a plane parallel to its base. The complete cone has height h₁ (marked "height of cone"). The frustum below the cutting plane has height h (marked "height"), slant height l (marked "slant height") and the radii r₁ and r₂ of its two circular ends.]
| Slant height of frustum (l) | \( \sqrt{h^2 + (r_1 - r_2)^2} \) |
|---|---|
| Lateral surface area | π(r₁ + r₂)l |
| Total surface area | π{(r₁ + r₂)l + r₁² + r₂²} |
| Volume | \( \frac{\pi}{3} \) (r₁² + r₁r₂ + r₂²)h |
| Height of cone of which the frustum is part (h₁) | \( \frac{h r_1}{r_1 - r_2} \) |
Here r₁ and r₂ are the radii of the two circular ends of the frustum, taking r₁ as the larger radius.
IMPORTANT FORMULAS & CONCEPT
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Useful Resources and Notes for Class 10 Mathematics Chapter 12 Surface Area and Volume
Core Study Kit: Class 10 Mathematics Chapter 12 Surface Area and Volume
Explore essential learning tools for Class 10 Mathematics Chapter 12 Surface Area and Volume. This curated collection features in-depth notes and targeted practice questions built around the active 2026 curriculum to streamline your daily revision.
NCERT-Aligned Solutions for Chapter 12 Surface Area and Volume
Each resource draws directly from authorized textbooks to maintain academic accuracy. Evaluating solved examples allows Class 10 students to master the formal presentation and answer-writing standards expected in upcoming school exams.
Next Steps in Your Exam Preparation
Maximize your grade potential by utilizing Class 10 Mathematics practice papers in tandem with these structured notes. All printable assignments and interactive mock tests on our platform are updated for the 2026 session and available free of charge.
FAQs
Our advanced study package for Chapter 12 Surface Area and Volume includes detailed concepts, diagrams, Mind Maps, and explanation of complex topics to ensure Class 10 students learn as per syllabus for 2026 exams.
The Mind Maps provided for Chapter 12 Surface Area and Volume act as visual anchors which will help faster recall during high-pressure exams.
Yes, teachers use our Class 10 Mathematics resources for lesson planning as they are in simple language and have lot of solved examples.
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Yes, our subject matter experts have updated the Chapter 12 Surface Area and Volume material to align with the rationalized NCERT textbooks and have removed deleted topics and added new competency-based questions.