Circumference of a Circle
A circle is a path taken by a
point which moves in such a way that its distance from a fixed point, in a
plane, is always constant. The fixed point is called the centre and the
distance between the moving point and the fixed point is called the radius.
The distance covered to go round a
circle once is called circumference.
The ratio of the circumference of a circle and its diameter is always constant.
Let us try to verify the result using
the following activity.
Activity: Rim of all the vehicles is circular. Different
types of vehicles are parked in the school parking lot such as bicycle, bus, car,
scooter and the size of the rim of each vehicle is different. Use a thread to
measure the circumference of circular rim of four different types of vehicles.
Also, measure the length of the diameter of each rim and tabulate the data as
follows:
|
Rim (circle) |
Circumference (c) |
Diameter (d) |
c/d |
|
Bicycle |
|
|
|
|
Bus |
|
|
|
|
Car |
|
|
|
|
Scooter |
|
|
|
Now, find the ratio of the circumference and the diameter for each rim (circle).
You will observe that in each
case, the ratio between the circumference and the diameter is always 22/7.
This ratio is known as π (pie).
Thus, we have
Circumference/Diameter
= π
Circumference = Ï€ × diameter
= Ï€ × 2r (Diameter = 2 × radius)
Thus, Circumference of a circle = 2Ï€r
Where Ï€ ≈ 3.14 or 22/7 approximately.
The constant π is an irrational
number. Its approximate value is 22/7. Unless otherwise stated, we shall take
the value of π as 22/7.
Circumference of a Circle Formula
Circumference of a
circle = 2Ï€r
Example 1: Find the circumference of a circle
with radius 7 cm.
Solution: Here,
r = 7 cm
We know that,
Circumference of a circle = 2Ï€r
=
2Ï€r = 2 × 22/7 × 7 cm
=
44 cm
Example 2: Find
the circumference of a circle with diameter 21 cm.
Solution: Here,
diameter = 14 cm, therefore, r = 21/2 = 10.5 cm
Circumference of a circle = 2Ï€r =
2 × 22/7 × 10.5
= 66 cm
Example 3: A
piece of wire, which is in the shape of a rectangle having length of 80
cm and breadth of 52 cm, is reshaped
and bent into the form of a circle. Find the
radius of the circle.
Solution: Given:
Length of the rectangle = 80 cm and breadth of the rectangle = 52
cm
Perimeter of the rectangle = 2(80 + 52)
cm = 264 cm
⇒ Circumference of
the circle = 264 cm
⇒ 2Ï€r = 264
⇒ r = 264/2Ï€
⇒ r = 132/Ï€
= 132 × 7/22 = 42 cm
Radius of the circle = 42 cm
Example 4: The radius of a wheel of a car is 49 cm. How many revolutions will the
Wheel complete to travel 154 km.
Solution: We
have, radius of the wheel of the car = 49 cm
Circumference of the wheel of the car
= 2Ï€r = 2 × 22/7 × 49
= 308 cm
Distance travelled by the car in one
revolution of the wheel = 308 cm
Total distance covered by the car = 154
km = 154 × 1000 × 100 cm = 15400000 cm
Number of revolutions = 15400000/308 =
50,000
Thus, the wheel will complete 50,000
revolutions to travel 154 km.