NCERT Class 10 Mathematics Mathematics: Chapter 12 — 1 Introduction
This chapter, 'Surface Areas and Volumes', revisits basic solids like cuboids, cones, cylinders, and spheres, along with their surface area and volume calculations from Class IX. It introduces objects formed by combining these basic shapes, such as a truck container (cylinder with hemispheres) and a test tube (cylinder with a hemisphere). The chapter explains how to calculate the surface area of such composite solids by summing the curved surface areas of their individual components. For instance, the surface area of a cylinder with hemispheres at both ends is the sum of the curved surface areas of the cylinder and the two hemispheres. This approach helps students tackle problems involving complex shapes encountered in real life, enhancing their understanding of geometry and its applications in CBSE mathematics.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 10 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 12 — 1 Introduction |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 460 |
Learning outcomes
- Identify basic solid shapes (cuboid, cone, cylinder, sphere).
- Understand that complex solids can be formed by combining basic solids.
- Calculate the surface area of composite solids by summing the surface areas of individual components.
- Apply knowledge of surface area and volume calculations to real-world objects.
Vocabulary
| Word | Meaning |
|---|---|
| Cuboid | A solid figure bounded by six rectangular faces. |
| Cone | A solid figure with a circular base and a curved surface tapering to a point (vertex). |
| Cylinder | A solid geometric figure with straight parallel sides and a circular or oval cross section. |
| Sphere | A perfectly round geometrical object in three-dimensional space. |
| Hemisphere | Half of a sphere. |
| Surface Area | The total area of the surface of a three-dimensional object. |
| Volume | The amount of space that a substance or object occupies. |
| Composite Solid | A solid formed by combining two or more basic solid shapes. |
| Curved Surface Area (CSA) | The area of the curved surface of a solid, excluding the areas of its bases. |
| Total Surface Area (TSA) | The sum of the areas of all the surfaces of a solid, including its bases. |
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Practice questions
- What are the basic solid shapes mentioned in the chapter? Answer: Cuboid, cone, cylinder, and sphere.
- How is the surface area of a composite solid generally calculated? Answer: By summing the curved surface areas of its individual components.
- Give an example of a composite solid mentioned in the text. Answer: A truck container made of a cylinder with two hemispheres at its ends, or a test tube made of a cylinder and a hemisphere.
Frequently asked questions
What is the main focus of NCERT Class 10 Mathematics Chapter 12?
The chapter focuses on calculating the surface areas and volumes of solids formed by combining basic shapes like cylinders, cones, and spheres.
What are the basic solid shapes covered in this chapter?
The chapter revisits cuboid, cone, cylinder, and sphere.
How do you find the surface area of a composite solid like a truck container?
You sum the curved surface areas of its individual parts, such as the cylinder and the two hemispheres.
What is the difference between TSA and CSA?
TSA (Total Surface Area) is the area of all surfaces, while CSA (Curved Surface Area) is the area of only the curved surfaces, excluding bases.
Where can I find the NCERT Class 10 Mathematics Chapter 12 PDF?
The NCERT Class 10 Mathematics Chapter 12 PDF can be downloaded from the official NCERT website or other educational portals.
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NCERT Class 10 Mathematics — Mathematics — Chapter 12 — 1 Introduction. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.