Circles calculate area circumference radius and diameter :
Here we are going to see some example problems to understand how to calculate area and circumference of circle.
The radius is a line segment with one end point at the centre and the other end on the circle. It is denoted by ‘r’.
Diameter is a chord passing through the centre of the circle. It is denoted by ‘d’.
The diameter is the longest chord. It is twice the radius.(i.e. d = 2r )
Circumference of a circle:
Can we find the distance covered by an athlete if he takes two rounds on a circular track. Since it is a circular track, we cannot use the ruler to find out the distance.
The distance around a circle is called the circumference of the circle, which is denoted by ‘C’. i.e., The perimeter of a circle is known as its circumference.
Circumference of circle = 2 π r
Area of circle :
The area of a circle is the number of square units inside that circle
Area of circle = π r²
Example 1 :
Find out the circumference of a circle whose diameter is 21 cm.
Diameter = 21 cm
Radius = 21/2 = 10.5 cm
Circumference of circle = 2 π r
= 2 (22/7) x 10.5
= 44 x 1.5
= 66 cm
Hence the circumference of circle is 66 cm.
Example 2 :
A wire of length 88 cm is bent as a circle. What is the radius of the circle.
Length of the wire = circumference of the circle
2 π r = 88 cm
2 x (22/7) x r = 88
r = (88 x 7)/(2 x 22)
r = 14 cm
Hence the radius of the circle is 14 cm
Example 3 :
The diameter of a bicycle wheel is 63 cm. How much distance will it cover in 20 revolutions?
When a wheel makes one complete revolutions,
Distance covered in one rotation = Circumference of wheel
Circumference of the wheel = 2πr units
= 2 x (22/7) x (63/2) cm
= 22 x 9 = 198 cm
For one revolution, the distance covered = 198 cm
For 20 revolutions, the distance covered = 20 × 198 cm
= 3960 cm
= 39 m 60 cm [100 cm = 1 m]
Hence the distance covered in 20 revolution is 39 m 60 cm
Example 4 :
A scooter wheel makes 50 revolutions to cover a distance of 8800 cm. Find the radius of the wheel.
= Number of revolutions/Circumference
2πr = 8800/50
2πr = 176
2 x (22/7) x r = 176
r = 176 x (7/22) x (1/2)
r = 28 cm
Hence the radius of the wheel is 28 cm
Example 5 :
The radius of a cart wheel is 70 cm. How many revolution does it make in travelling a distance of 132 m.
Given: r = 70 cm, Distance travelled = 132 m.
Circumference of a cart wheel = 2πr
= 2 x (22/7) x 70
= 440 cm
= Number of revolutions x Circumference
Number of revolutions
= Distance travelled/Circumference
= 132 m/440 cm
Hence the number of revolution is 30.
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