Circumference of a circle is the distance around the circle.
Formula :
Circumference of Circle = 2πr
Here the value of π is either 22/7 or 3.14 and "r" stands for radius of a circle.
Example 1:
Find the circumference of a circle whose radius is 14 cm.
Solution:
Formula for circumference of circle is
= 2πr
Substitute π = 22/7 and r = 14.
≈ 2 x (22/7) x 14
= 2 x 22 x 2
= 88
So, circumference of the given circle is about 88 cm.
Example 2:
Find the diameter of circle with circumference is 88 cm.
Solution:
Circumference of circle = 88 cm
2πr = 42
2 x (22/7) x r = 42
(44/7) x r = 42
Multiply each side by 7/44.
r = 88 x (7/44)
r = 2 x 7
r = 14
Then, diameter is
= 2 x radius
= 2 x 14
= 28 cm
Example 3 :
Find the circumference of a circle with an area of 441π square feet.
Solution :
Area of the circle = 441π ft^{2}
πr^{2 }= 441π
Divide each side by π.
r^{2} = 441
r = 21
Formula for circumference of circle is
= 2πr
Substitute π = 22/7 and r = 21.
≈ 2 x (22/7) x 21
= 2 x 22 x 3
= 132
So, circumference of the given circle is about 132 ft.
Example 4 :
The moon is about 384000 km away from the earth and its path around the earth is nearly circular. Find the distance traveled by the moon every month.
Solution :
Because the path of the moon around the earth is nearly circle, the distance traveled by the moon every month is the circumference of the circle.
Given : The moon is about 384000 km away from the earth
Then radius is 384,000.
Formula for circumference of circle is
= 2πr
Substitute π = 22/7 and r = 38400.
≈ 2 x 3.14 x 384,000
= 2,411,520
So, the distance traveled by the moon every month is about 2,411,520 km.
Example 5 :
A copper wire is in the form of a circle with radius 35 cm. If it is bent into a square, find the length of each side of the square.
Solution :
Given : Radius of a circle is 35 cm.
Since the same wire is bent into the form of a square,
Circumference of the circle = Perimeter of the square
Circumference of circle is
= 2πr
Substitute π = 22/7 and r = 35.
≈ 2 x (22/7) x 35
= 2 x 22 x 5
= 220
Then,
perimeter of the square = 220 cm
4a = 220
Divide each side by 4.
a = 55
So, the length of each side of the square is 55 cm.
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