# CLASS-9CIRCUMFERENCE & 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

22

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

7

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

22

Or,  2 X ------ X r = 308

7

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

22

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

7

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

22

Or, ---------- X r² = 246.4

7

246.4 X 7

Or,   r² =  ------------ = 78.4 cm²

22

Or,   r = √78.4 cm = 8.85 cm                                                                                                             22

Now, the circumference of the circle = 2πr2 X ------ X 8.85

7

=  55.44 cm

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