NCERT Class 10 Math Chapter 11: वृत्तों से संबंधित क्षेत्रफल PDF Download

NCERT Class 10 Math Chapter 11 वृत्तों से संबंधित क्षेत्रफल (Areas Related to Circles) explains how to calculate areas of circle segments, sectors, and combined shapes. The chapter builds on what students already know about circles and geometry, and applies it to real-life problems like finding the area of flower beds, playground tracks, or shaded

NCERT Class 10 Math Chapter 11 वृत्तों से संबंधित क्षेत्रफल (Areas Related to Circles) explains how to calculate areas of circle segments, sectors, and combined shapes. The chapter builds on what students already know about circles and geometry, and applies it to real-life problems like finding the area of flower beds, playground tracks, or shaded regions in diagrams. These concepts are very practical because they combine geometry with mensuration, helping students understand applications of mathematics in daily life.

I chose to write about this chapter because it often looks simple at first glance but students tend to make mistakes in applying formulas, especially when it comes to areas of sectors and segments. Many board exam questions are designed around this chapter, usually with diagrams where one has to calculate shaded portions by subtracting or adding different areas. For example, finding the area of a path around a circular garden or calculating the area of a semicircular design is a common type of problem. By mastering this chapter, students not only score well in exams but also develop a better understanding of how mathematics is used to solve practical geometry-based problems. Having the NCERT PDF makes it easy to revise formulas and go through solved examples to build confidence.

Key Concepts in Chapter 11 वृत्तों से संबंधित क्षेत्रफल

This chapter mainly covers:

Area of a circle using the formula πr²
Area of sector of a circle = (θ/360) × πr²
Area of segment of a circle (using sector area minus triangle area)
Application-based problems involving combinations of circles with squares, rectangles, and triangles

Example for Practice

If the radius of a circle is 7 cm, then the area of a semicircle is (½ × π × r²) = 77 cm² (using π = 22/7). Such questions are often asked in board exams.

Download PDF

Students can download NCERT Class 10 Math Chapter 11: वृत्तों से संबंधित क्षेत्रफल PDF from this 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.