**Area of a circle : **

In this section, we are going to see how to find the area
of a circle. This page contains formulas, example problems and also
practice questions to understand this topic in a better way.

**Area :**

Area of the circle means 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

Therefore 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 ) x (14)²

= ( 22/7 ) x 14 x 14

= 22 x 2 x 14

= 44 x 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) x r² = 616

r² = (616 x 7) /22

r² = (616 x 7) /22

r² = 28 x 7

r² = √(2 x 2 x 7 x 7)

r = 2 x 7

r = 14 cm

Diameter = 2 x radius

= 2 x 14

= 28 cm

Therefore 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 ) x ( 21 )²

= (22/7) x 21 x 21

= 22 x 3 x 21

= 66 x 21

= 1386 cm²

Therefore the area of the given circle is 1386 cm²

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**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**

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