For a circle with radius r
Area of circle will be
Area of circle = π r 2
Here,
π can be taken as
π = 3.14 or π = 22/7
Let’s take some examples
Find area of circle of radius 2 cm by counting squares , and also by formula
|
Covered Area |
Number |
Area |
|
|
1 |
Fully - filled squares |
4 |
1 × 4 = 4 |
|
2 |
Half - filled squares |
0 |
1/2 × 0 = 0 |
|
3 |
More than Half - filled squares |
8 |
1 × 8 = 8 |
|
4 |
Less than Half - filled squares |
4 |
0 × 4 = 0 |
Area = 4 + 0 + 8 + 0
= 12 cm 2
By formula of area of circle
Area = πr 2
= 3.14 × (2) 2
= 3.14 × 4
= 314/100 × 4
= 1256/100
= 12.56 cm 2
So, finding area by formula is more accurate
Find area of a circle with radius of 3.5 cm
Radius = r = 3.5 m
Area = πr 2
= π (3.5) 2
= 22/7 × (35/10) 2
= 22/7 × (7/2) 2
= 22/7 × 7/2 × 7/2
= 11/7 × 7/1 × 7/2
= 11/1 × 1 × 7/2
= 77/2
= 38.5 cm 2
∴ Area is 38.5 cm 2
Find area of a circle whose radius of 7 cm
Radius = r = 7 cm
Area = π r 2
= 22/7 × (7) 2
= 22/7 × 7 × 7
= 22 × 7
= 154 cm 2
∴ Area is 154 cm 2
Find area of a circle with diameter 21 cm
Diameter = 21 cm
Radius = r = Diameter/2
= 21/2 cm
Now,
Area = π r 2
= 22/7 × (21/2) 2
= 22/7 × 21/2 × 21/2
= 11/7 × 21/1 × 21/2
= 11/1 × 3 × 21/2
= (33 × 21)/2
= 693/2
= 346.5 cm 2
∴ Area is 346.5 cm 2
Find area of a circle with diameter 42 cm
Diameter = 42 cm
Radius = r = Diameter/2
= 42/2 cm
= 21 cm
Now,
Area = π r 2
= 22/7 × (21) 2
= 22/7 × 21 × 21
= 22/1 × 3 × 21
= 66 × 21
= 1386 cm 2
∴ Area is 1386 cm 2
Find area of a circle with radius 5 cm
Radius = r
= 5 cm
Now,
Area = π r 2
= 3.14 × (5) 2
= 3.14 × 25
= 314/100 × 25
= 314/20 × 5
= 314/4 × 1
= 157/2
= 78.5 cm 2
∴ Area is 78.5 cm 2
Find the area of a circle with diameter 30 cm
Diameter = 30 cm
Radius = r = Diameter/2
= 30/2 cm
= 15 cm
Now,
Area = π r 2
= 3.14 × (15) 2
= 3.14 × 225
= 314/100 × 225
= 314/20 × 45
= 157/10 × 45
= 7065/10
= 706.5 cm 2
∴ Area = 706.5 cm 2
