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

Free Demo Classes

Register here for Free Demo Classes

Please fill the name
Please enter only 10 digit mobile number
Please select course
Please fill the email

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
Important Questions for Class 10 Maths Chapter 12 Areas Related to Circles 1

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
Important Questions for Class 10 Maths Chapter 12 Areas Related to Circles 2

The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

Important Questions for Class 10 Maths Chapter 12 Areas Related to Circles 5

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.

Important Questions for Class 10 Maths Chapter 12 Areas Related to Circles 13

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
Important Questions for Class 10 Maths Chapter 12 Areas Related to Circles 15

Free E Books