AREA OF A CIRCLE
Area of a circle :
Area of the circle stands for surface occupied by the figure.
In the above shape, the part filled with red color is called area of a circle.
Formula :
Area = Π r ²
Here the value of Π is either 22/7 or 3.14 and "r" is known as the radius of a circle. Now let us see some example problems.
Example 1:
Find the area of the circle which is having the radius 21 cm.
Solution :
In this problem we need to find the area of the circle having a radius 21 cm. We need to apply this value instead of r in the formula.
Area of circle = Π r ²
= (22/7 ) x ( 21 )²
= (22/7) x 21 x 21
= 22 x 3 x 21
= 66 x 21
= 1386 cm²
Hence the area of the given circle is 1386 cm²
Example 2:
Find the area of the circle which is having the diameter 28 cm.
Solution :
To find the area first we need to find the radius of the circle from the diameter.
Diameter = 28 cm
Radius = diameter/2
= 28/2
= 14 cm
Area of circle = Π r ²
= (22/7) ⋅ (14)²
= (22/7) ⋅ 14 ⋅ 14
= 22 ⋅ 2 ⋅ 14
= 44 ⋅ 14
= 616 cm²
Example 3 :
The area of a circular region is 616 cm². Then find its diameter.
Solution :
Area of circle = 616 cm²
Π r ² = 616 cm²
(22/7) ⋅ r² = 616
r² = (616 ⋅ 7) /22
r² = (616 ⋅ 7) /22
r² = 28 ⋅ 7
r = √(2 ⋅ 2 ⋅ 7 ⋅ 7)
r = 2 ⋅ 7
r = 14 cm
Diameter = 2 ⋅ radius
= 2 ⋅ 14
= 28 cm
Hence the diameter of the given circle is 28 cm.
Example 4 :
Find the length of the rope by which a cow must be tethered in order that it may be able to graze an area of 9856 sq.meters
Solution :
In this problem we need to find the area of the circle having a radius 21 cm. We need to apply this value instead of r in the formula.
Area of circle = Π r ²
= (22/7) ⋅ ( 21 )²
= (22/7) ⋅ 21 ⋅ 21
= 22 ⋅ 3 ⋅ 21
= 66 ⋅ 21
= 1386 cm²
Hence area of the given circle is 1386 cm²
Related Topics
- perimeter of sector
- Length of arc
- Practice questions on length of arc
- Perimeter of square
- Perimeter of parallelogram
- Perimeter of rectangle
- Perimeter of triangle
- Area of a circle
- Area of Semicircle
- Area of Quadrant
- Area of sector
- Area of triangle
- Area of equilateral triangle
- Area of scalene triangle
- Area of square
- Area of rectangle
- Area of parallelogram
- Area of rhombus
- Area of trapezium
- Area of quadrilateral
- Area around circle
- Area of pathways
- Area of combined shapes
After having gone through the stuff above, we hope that the students would have understood area of a circle.
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