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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