CLASS-9
CIRCUMFERENCE & AREA OF CIRCLE

CIRCUMFERENCE & AREA OF CIRCLE –

For every circle circle, the ratio between the circumference and diameter in a constant. This constant is represented by a Greek letter π (Pi)

Circumference

So, π = -----------------

Diameter

1. For a circle of radius = r units, we have

(i) Circumference of the circle = 2πr units = πd units

Where d is the parameter, and d = 2r

(ii) Area of a circle = πr² sq.units

There are some example are given below for your better understanding –

Example.1) Calculate the circumference and area of a circle of radius 8.4 cm

Ans.) Circumference of the circle = 2πr

= 2 X ------- X 8.4 = 2 X 22 X 1.2 = 52.8 cm² (Ans.)

Example.2) The circumference of a circle is 180.6 cm, calculate the following –

i) The radius of the circle in cm

ii) The area of the circle, correct the nearest cm²

Ans.) Let the radius of the circle be r cm

Then its circumference will be = 2πr cm

As per the given condition –

2πr = 180.7

Or, 2 X ------ X r = 308

308 X 7

Or, r = ------------ = 7 X 7 = 49 cm ..................(i) (Ans.)

22 X 2

ii) Now, as we know the formula area of circle is = πr²

so, πr² = ------ X (49)² = 22 X 7 X 49 = 7546 cm²...........(ii) (Ans.)

Example.3) The area of a circle is 246.4 cm². Find the circumference of the circle.

Ans.) According to the given condition area of the circle is 246.4 cm². As per the formula of area of circle is πr² (where r = radius of circle).

So, πr² = 246.4

Or, ---------- X r² = 246.4

246.4 X 7

Or, r² = ------------ = 78.4 cm²

Or, r = √78.4 cm = 8.85 cm 22

Now, the circumference of the circle = 2πr = 2 X ------ X 8.85

= 55.44 cm

So, circumference of the circle, correct to nearest cm = 55 cm (Ans.)

CLASS-9CIRCUMFERENCE & AREA OF CIRCLE