# NCERT CBSE Class 10th Mathematics Chapter 12: Areas Related to Circles

Safalta Expert Published by: Sylvester Updated Wed, 22 Jun 2022 06:52 PM IST

## Highlights

NCERT CBSE Class 10th Mathematics Chapter 12: Areas Related to Circles

The twelfth chapter in Mathematics textbook is 'Areas Related to Circles'.

### Minor arc and Major Arc

An arc length is called a major arc if the arc length enclosed by the two radii is greater than a semi-circle.

### Sector of a Circle and its Area

A region of a circle is enclosed by any two radii and the arc intercepted between two radii is called the sector of a circle.

### Minor Segment

The region enclosed by an arc and a chord is called a segment of the circle. The region enclosed by the chord PQ & minor arc PRQ is called the minor segment.
Area of Minor segment = Area of the corresponding sector – Area of the corresponding triangle

### Major Segment

The region enclosed by the chord PQ & major arc PSQ is called the major segment.
Area of major segment = Area of a circle – Area of the minor segment

### The topics discussed in this chapter are as follows:

• Area of a circle
• Circumference of a circle
• Segment of a circle
• Sector of a circle
• Angle of a sector
• Length of an arc of a sector
• Area of sector of a circle
• Area of triangle
• Area of segment of a circle

## The circumference of a circle is 22 cm. Calculate the area of its quadrant (in sq. cm)

Circumference of a circle = 22 cm 2πr = 22 cm ## If the difference between the circumference and the radius of a circle is 37 cm, then using π = 22/7, calculate the circumference (in cm) of the circle.

2πr – r = 37 ⇒ r(2π – 1) = 37 ## The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes. ## Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions 14 cm × 7 cm. Find the area of the remaining card board. Here r = 7/2 cm, L = 14 cm, B = 7 cm
Area of the remaining card board
= ar(rectangle) – 2(area of circle)
= L x B – 2πr2)
= 14 × 7 – 2 × 22/7 × 7/2 × 7/2
= 98 – 77 = 21 cm2

## Area of a sector of a circle of radius 14 cm is 154 sq. cm. Find the length of the corresponding arc of the sector.

Area of sector = 154 cm2 