Area of Circle

1. Area of Circle

2. Relationship between diameter and radius: Diameter of a circle is twice of its radius. Formula: • Diameter = 2 x radius • Radius = r O r B A d

3. Pi (π) The ratio of circumference to diameter is constant for all circles. This ratio is called Pi and is written as π. Where π= C ⇒ = π ⇒ C = πd C = 2πr d 22 7

4. Area of a circle The area of a circle is given by the formula Area of the circle = πr² sq. units

5. Example 1: Find the area of a circle whose radius is 7 cm. Solution Given:- radius(r) = 7 To Find :- area of circle Area (A) = πr² Divide 7 and 7 by 7 A = 22 x 7 = 154 cm

6. Example 2: Find the radius of a circle whose area is 616 m2. Solution Given:- Area = 616 m2To Find :- Radius Area (A) = πr² 22 x r2 = 616 x 7 Taking 7 to the other side 28 308 Divide 22 and 616 by 2 Taking 22 to the other side 11 1 Divide 11 and 308 by 11 r2 = 28 x 7 = 196 Taking prime factors of 196, we get r2 = 7 x 7 x 2 x 2 = 72 x 22 = (7 x 2)2 Ans: r = 14 m r = 14 m Cancelling the powers, we get

7. Example 3: Find the area of a circle whose diameter is 42 cm. Solution Given:- Diameter =42cm To Find:- Area of circle since radius(r) is not given we find radius(r) using diameter Now we have found radius, Lets us now calculate area of circle We know that Area = πr² 3 Divide 21 and 7 by 7 Area = 22 x 3 x 14 = 924 cm2(Ans)

8. Example 4: Find the diameter of a circle whose area is 154 cm2. Solution Given:- Area = 154 cm2To Find :- Diameter Area (A) = πr² To find diameter, we need to find radius first 22 x r2 = 154 x 7 Taking 7 to the other side 7 77 Divide 22 and 616 by 2 Taking 22 to the other side 11 1 Divide 11 and 308 by 11 r2 = 7 x 7 = 72 r = 7 cm Cancelling the powers, we get Ans: d = 14 cm So, Diameter = 2 x radius = 2 x 7 = 14 cm

9. Try these • Find the area of a circle whose diameter is 21 cm. • Find the area of the circle whose radius is 56 cm.