## Area of Circle

Consider the circle below with a radius ‘r’. Area of a circle, in lay terms, is the amount of region enclosed by the green curve going round the point C.

Area of a circle, technically, is Π times the radius squared.

i.e. Area of a circle = Π × r2.

Area of a circle, if diameter length is d, is Π × (d2/4).

{since radius is half of diameter}

Write either 22/7 or approximately 3.14 for Π

Let us solve a few questions on area of a circle, when different parameters are given

Example 1:

Find the area of a circle whose radius is 7 cms.

Substitute 7 in radius, r in the area of a circle, Π × r2.

So, area of circle is Π × 72 = (22/7) × 497 = 22 × 7 = 154.

Expressed along with units, the area of circle is 154 sq. cms.

Example 2

Find the area of a circle whose circumference is 88 cms.

Using the formula for circumference of a circle 2Πr, let us find radius r:

Since, 2Πr = 88, therefore, 2 × (22/7) × r = 88,

finally, r = (288 × 7)/44 = 14 cms.

Now, substituting 14 in r in the formula for area of circle, Πr2,

The area will be (22/7) × 142 = (22/7) × 214 ×14 = 22 × 28 = 616

Expressed with units, the area of circle above is 616 sq cms.

Example 3 Four coins, each of radius 2 cms are placed inside a circular board of diameter 6 cms as shown above. The coins just touch each other and the board. Approximately what percentage of the board in the above figure is shaded?

Area of each circular coin having radius 2 cms is Π × 22 = 4Π,

So, area of all 4 circular coins = 4 × 4Π = 16Π

Area of the circular board having radius 6 cms = Π × 62 =36 Π

Therefore, area of the circular board not occupied by the four circular coins = 36 Π - 16 Π = 20 Π.

Therefore, percentage of the area of the circular board shaded will be

(20 Π/36 Π) ×100% = (520/936) × 100% =

(5/9) ×11 100% = 55% approximately.