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So, Circumference(C) =π
Diameter()
d
Thus, Circumference, C = p × diameter (d)
Or C = p × d
But, d = 2 × r (Q Diameter = 2 × Radius)
Thus, C = 2pr (where r is the radius of the circle)

Maths Talk
Draw a few number of circles each of different radius. Find their diameters and circumferences. Also, find the ratio
C
between the circumference and diameter, . Is it the same in all cases? Discuss.
d
Example 18: What is the circumference of a circular disc of radius 21 cm?    Take π= 22  .


7
Solution: Radius of circular disc (r) = 21 cm

We have, circumference of a circle = 2pr = 2 × 22 × 21 cm
7
= 2 × 22 × 3 cm = 132 cm
Thus, the circumference of the circle of radius 21 cm is 132 cm.

Example 19: The diameter of a scooter wheel is 56 cm. How much distance will it cover in 20
revolutions?

Solution: Circumference of a scooter wheel = 2pr (Q C = 2pr)


= 2 × 22 × 28 cm = 176 cm Q r = d = 56 cm = 28 cm 


7  2 2 
Q The distance covered by the wheel in one revolution = circumference of the wheel
\ The scooter wheel will cover 176 cm in one revolution.

So, the distance covered in 20 revolutions = (20 × 176) cm = 3520 cm = 35 m 20 cm or 35.20 m
Example 20: Circumference of a circle is 154 cm. Find the diameter of the circle.

Solution: Let r be the radius of the circle.

We have, circumference of a circle = 2pr

154 cm = 2 × 22 × r
7
×
154 7 49
r = cm = cm
×
222 2
Therefore, the diameter of the circle = 2 × 49 cm = 49 cm (Q d = 2 × r)
2
Thus, the diameter of the circle is 49 cm.
Example 21: The inner circumference of a circular track is 220 m and the width of the track is 3.5
m. Calculate the cost of putting up a fence along the outer circle of the track at the rate of `60 per m.

295 Perimeter and Area