Grade -IX

1. By
Sri. Siddalingeshwara BP M.Sc, B.Ed, (P.hd)
AREAS RELATED TO CIRCLES
Chapter-10
for
class-x

2.  Content:
1.Perimeteer and Area of a Circle.
Area of a Circle
Parts of Circle
Circumference of a Circle
2.Areas of sector and segment of a Circle.
Segment of a circle
Sector of a Circle
Angle of a Sector
Length of an arc of a sector
Area of a Sector of a Circle
3.Areas of combination of Plane Figures.

3. 1. PERIMETER AND AREA OF A CIRCLE
 Area of a Circle
Area of a circle is π𝑟2, where π=22/7 or ≈3.14 (can be used
interchangeably for problem-solving purposes)and r is the
radius of the circle.
π is the ratio of the circumference of a circle to its diameter.

5.  Circumference of a Circle
The perimeter of a circle is the distance covered by going
around its boundary once. The perimeter of a circle has a
special name: Circumference, which is π times the diameter
which is given by the formula 2πr
𝑐𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒
𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟
= π
Circumference= π x diameter
= π x 2r
(where r is the radius of the circle)
= 2 πr
( By Aryabhatta)
The Value of π = 3.1416 or 22/7
(By Srinivas Ramanujam)

6. 2.AREAS OF SECTOR AND SEGMENT OF A CIRCLE
• Segment of a circle
A circular segment is a region of a circle which is “cut off”
from the rest of the circle by a secant or a chord.
• Sector of a Circle
A circle sector/ sector of a circle is defined as the region of
a circle enclosed by an arc and two radii. The smaller area is
called the minor sector and the larger area is called the major
sector.
• Angle of a Sector
The angle of a sector is that angle which is enclosed
between the two radii of the sector.

7.  Sector and segment:

8.  Length of an arc of a sector
The length of the arc of a sector can be found by using the
expression for the circumference of a circle and the angle of the
sector, using the following formula:
L= (θ/360°)×2πr
Where θ is the angle of sector and r is the radius of the circle.
 Area of a Sector of a Circle
Area of a sector is given by
(θ/360°)×π𝑟2
where ∠θ is the angle of this sector(minor sector in the following
case) and r is its radius
 Perimeter of the Sector: (θ/360°)×2πr+2r

9. Now let us take the case of the area of the segment APB of circle with
Centre O and radius r as shown in figure
Such that
Area of the segment APB = Area of the sector OAPB- Area of the triangle OAB
𝜃
3600 Xπ𝑟2
− 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 𝑂𝐴𝐵
• Area of the major sector OAQB = π𝑟2
− Area of the minor sector OAPB
• Area of major segment AQB = π𝑟2
− Area of the minor segment APB

11. 3. Areas of combination of plane figures:
It’s a combination of geometric plane figures
some standard plane figures with shaded area marked:
To find the area of the shaded region in
 1. Shape A: find the difference between the area of the larger
circle and the area of the smaller circle
 2. Shape B: find the area of the square and then subtract the
area of the circle
 3. Shape C: Subtract the area of the rectangle from the area of
the circle
 4. Shape D: Difference between the area of the rectangle and
the triangle gives the area of the shaded region

12.  For Example:

13. References:
1.NCERT Text book
2.Google Sources
Thank you