NCERT Class 10 Math Chapter 12: पृष्ठीय क्षेत्रफल और आयतन PDF Download

NCERT Class 10 Math Chapter 12 पृष्ठीय क्षेत्रफल और आयतन (Surface Areas and Volumes) focuses on three-dimensional geometry and its applications. This chapter covers formulas and problem-solving methods related to cubes, cuboids, cones, spheres, hemispheres, and cylinders. It also deals with conversion of solids from one shape to another and problems involving combinations of different

NCERT Class 10 Math Chapter 12 पृष्ठीय क्षेत्रफल और आयतन (Surface Areas and Volumes) focuses on three-dimensional geometry and its applications. This chapter covers formulas and problem-solving methods related to cubes, cuboids, cones, spheres, hemispheres, and cylinders. It also deals with conversion of solids from one shape to another and problems involving combinations of different solids. These concepts are useful not only in board exams but also in real life, such as calculating paint needed for a wall, water capacity of a tank, or material required for making containers.

I decided to write about this chapter because it is one of the most practical and scoring parts of the Class 10 syllabus. Students often find it interesting as they can directly relate it to daily life. However, many get confused while applying the correct formulas, especially when shapes are combined or converted. For instance, finding the volume of melted metal recast into new shapes or the surface area of a cone attached to a cylinder can feel tricky at first. That is why having the NCERT PDF is very helpful. It explains concepts with clear examples, provides solved exercises, and offers practice questions that strengthen understanding. With proper revision, this chapter becomes a strong scoring area in exams.

Key Concepts in Chapter 12 पृष्ठीय क्षेत्रफल और आयतन

This chapter includes:

Surface area and volume of cube, cuboid, sphere, hemisphere, cylinder, and cone
Surface area and volume of a frustum of a cone
Problems on conversion of solids (like melting and recasting)
Problems on combination of solids (like cone + hemisphere, cylinder + cone, etc.)

Example Problem

A solid metallic sphere of radius 7 cm is melted and recast into smaller spheres of radius 1 cm. The number of small spheres formed will be (Volume of big sphere ÷ Volume of small sphere). Such practical questions are common in exams.

Download PDF

Students can download NCERT Class 10 Math Chapter 12: पृष्ठीय क्षेत्रफल और आयतन PDF from this official website.

NCERT Class 10 Math Chapter 14: प्रायिकता PDF Download

NCERT Class 10 Math Chapter 14 प्रायिकता (Probability) introduces students to the concept of chance and likelihood of events. In this chapter, students learn how to calculate the probability of simple events using the formula P(E) = Number of favourable outcomes ÷ Total number of outcomes. The chapter deals with real-life examples like tossing a

NCERT Class 10 Math Chapter 14 प्रायिकता (Probability) introduces students to the concept of chance and likelihood of events. In this chapter, students learn how to calculate the probability of simple events using the formula P(E) = Number of favourable outcomes ÷ Total number of outcomes. The chapter deals with real-life examples like tossing a coin, rolling a dice, or drawing cards, which makes the subject more interesting and practical. Since probability questions are common in board exams and are generally considered easy, this chapter is highly important for scoring well.

I am writing about this topic because probability is not only an important part of the Class 10 syllabus but also a concept that students will use in higher studies and real life. From predicting weather conditions to calculating risks in business, probability plays a key role. Many students initially find it confusing, but NCERT presents it in a simple and easy-to-understand manner. By practising from the NCERT book, students can build a strong foundation and develop confidence in solving probability problems. Having the PDF makes it easier for learners to access the chapter anytime, revise formulas, and attempt practice questions before exams.