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.
Answer:
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.
Answer:
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?
Answer:
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.