Area of a Circle
The area of a circle refers to the amount of space covered by the circle. It totally depends on the length of its radius → Area = πr2 square units.
Circumference of a Circle
The circumference is the total length of the boundary of a circle → Circumference = 2πr units.
Examples
1. Find the area and the circumference of a circle whose radius is 10 cm. (Take the value of π = 3.14)
Solution:
Given: Radius = 10 cm.
Area =π r2
= 3.14 × 102
A= 314 cm2
Circumference, C = 2πr
C= 2 ×3.14× 10
Circumference= 62.8 cm
2. Find the area of a circle whose circumference is 31.4 cm.
Solution:
Given:
Circumference = 31.4 cm
To find the area of a circle, we need to find the radius.
From the circumference, the radius can be calculated:
2 π r = 31.4
(2)(3.14)r = 31.4
r = 31.4 /(2)(3.14)
r=10/2
r= 5
Therefore, the radius of the circle is 5 cm.
The area of a circle is πr2 square units
Now, substitute the radius value in the area of a circle formula, we get
A = π(5)2
A = 3.14 x 25
A = 78.5 cm2
Therefore, the area of a circle is 78.5 cm2.