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## NCERT Solutions for class 10 Maths Chapter 12

### 10th Maths Chapter 12 Exercise 12.1

### 10th Maths Chapter 12 Exercise 12.2

### 10th Maths Chapter 12 Exercise 12.3

Class: 10 | Maths (English and Hindi Medium) |

Chapter 12: | Areas related to Circles |

#### Class 10 Maths Chapter 12 Exercise 12.1 Solutions in Videos

### 10th Maths Chapter 12 Solutions

NCERT Solutions for class 10 Maths Chapter 12 Areas related to Circles all exercises are given below updated for new academic year 2022-2023 for all boards who are using NCERT Books as a course books. UP Board Students also can download UP Board Solutions for Class 10 Maths Chapter 12 in Hindi from here.

#### Class 10 Maths Chapter 12 Exercise 12.2 Solutions in Videos

#### Class 10 Maths Chapter 12 Exercise 12.3 Solutions in Videos

### NCERT Solutions for Class 10 Maths Chapter 12

- NCERT Solutions 10th MathsExercise 12.1Read more
- NCERT Solutions 10th MathsExercise 12.2Read more
- NCERT Solutions 10th MathsExercise 12.3Read more

#### Previous Years Questions

## Three Marks Questions

In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region. [CBSE 2017]

## Four Marks Questions

1. In the given figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square where O and O’ are the centres of the circles. Find the area of the shaded region. [CBSE 2017] 2. A chord PQ of a circle of radius 10 cm subtends an angle of 60 at the centre of circle. Find the area of major and minor segments of the circle. [CBSE 2017]

##### Objective of the Area Related to Circles

To find the circumference, area of a circle and circular paths. To derive and understand the formulae for perimeter and area of a sector of a circle. To find the perimeter and the area of a sector, using the above formulae. Finding the areas of some combinations of figures involving circles, sectors as well as triangles, squares, rectangles and solve daily life problems based on perimeters and areas of various plane figures.

###### Formulae for perimeters and areas

- Perimeter of a rectangle = 2 (length + breadth)
- Area of a rectangle = length × breadth
- Perimeter of a square = 4 × side
- Area of a square = (side) × (side)
- Area of a parallelogram = base × corresponding altitude
- Area of a triangle = 1/2 × base × corresponding altitude
- Area of a rhombus = 1/2 × product of its diagonals
- Area of a trapezium = 1/2 × (sum of the two parallel sides) × distance between them
- Circumference of a circle = 2 × π × radius
- Area of a circle = π × (radius) × (radius)
- Area of a sector = angle/360 × π × (radius) × (radius)
- Length of an arc = angle/360 × 2π × (radius)
- Perimeter of a sector = angle/360 × 2π × (radius) + 2(radius)
- Area of segment = Area of sector – area of triangle

###### Historical Facts!

- All the mathematical ideas have emerged out of daily life experiences. The first ever need of human being was counting objects. This gave rise to the idea of numbers. When the man learn to grow crops, following types of problems had to be handled:

Fencing or constructing some kind of a boundary around the field, where the crops were to be grown. - Allotting lands of different sizes for growing different crops.
- Making suitable places for storing different products grown under different crops.
- These problems led to the need of measurement of perimeters (lengths), areas and volumes, which in turn gave rise to a branch of mathematics known as Mensuration. Area related to circle is one of the part of mensuration.

### How many sums are there in class 10 Maths chapter 12 Areas Related to Circles?

There are 3 exercises in class 10 math chapter 12 (Areas Related to Circles).

In first exercise (Ex 12.1), there are only 5 questions.

In second exercise (Ex 12.2), there are in all 14 questions.

In third exercise (Ex 12.3), there are in all 16 questions.

So, there are in all 35 questions in class 10 math chapter 12 (Areas Related to Circles).

There are only 6 examples in class 10 math chapter 12 Areas Related to Circles.

Example 1 is based on Ex 12.1.

Examples 2, 3 are based on Ex 12.2.

Examples 4, 5, 6 are based on Ex 12.3.

### Which topics students should recall before starting 10th Maths chapter 12?

Before starting class 10 math chapter 12, Students should recall the following topics from chapter 10 (Circles) of class 9th math.

Topics: 1) Meaning of Chord of the circle.

2) Meaning of Arc (Major Arc and Minor Arc).

3) Meaning of Sector of the circle (Major Sector and Minor Sector).

4) Meaning of Segment of the circle (Major Segment and Minor Segment).

And some other things like radius of circle, diameter of circle etc.

### What students will study in chapter 12 Areas Related to Circles of class 10 Maths?

In chapter 12 Areas Related to Circles of class 10 math, students will study

1) Perimeter (circumference) of a circle and Area of a circle.

2) Areas of Sector and Segment of a Circle.

3) Length of an Arc of a sector of a circle.

4) Areas of Combinations of Plane Figures.

### Is chapter 12 Areas Related to Circles of class 10th Maths an easy topic?

Chapter 12 (Areas Related to Circles) of class 10th mathematics is not easy and not difficult, it lies in middle of easy and difficult because some examples and questions of this chapter are easy and some are difficult. But difficulty level of anything varies from student to student. So, Chapter 12 (Areas Related to Circles) of class 10th mathematics is easy or not depends on students also. Some students find it difficult some find it easy and some find it in middle of easy and difficult.

### How do we find area of circle and perimeter in 10th Maths Chapter 12?

Perimeter (circumference) of circle is 2πr, where r is the radius of circle. And Area of a circle is π r², where r is the radius of the circle.

Use the formula given above and find the area or perimeter directly.