Area of the circle

defination of the circle
and how to measure its area

1. السلام عليكم .......... معكم مستر عماد سامى Area of the circle

2. Q . What is the shape of these things? A . All the things are having circular shapes.

3. Q . What is the shape of this stadium? A .The shape of this stadium is circular.

4. Here is a circular garden and we want to find the l cost of planting grass in it, which thing we need to measure ? Area of circular garden.

5. AREA OF A CIRCLE Definition Important Terms Derivation of Formula Related Examples Daily Life Applications of Circle

6. Def inition The locus of points whose distance from a fixed point is always constant. The fixed point is called centre and is denoted by ‘O’.

7. Q AREA OF A CIRCLE Important Terms Radius The distance of any point on the circl e fr om the centre is called radius. It is denoted by ‘r’. OA is the radius of the circle. P Chord A line segment having end points on th e c ircle. In figure the line segment PQ is the chord of the circle. O r A .

8. AREA OF A CIRCLE Important Terms Diameter A ch o rd through t h e ce n tre o f a ci r cle i s ca l led diameter of the circle. The line segment PC is the diameter O . C P Arc The distance between two points on the boundary of circle is called an arc. e.g. CD is an arc. D

9. 7 and  = 22 = 3.1416 approximately. AREA OF A CIRCLE Important Terms Circumference The distance around a circle is called the circumference. The ratio of circumference of a circle to its diameter is constant and is denoted by a Greek letter  (pi)

10. by Where is the ratio between circumference and diameter of a circle. A  π r 2  AREA OF A CIRCLE Derivation of Formula The measure of plane region bounded by a circle is called its area. The area of a circle of radius r is given

11. Derivation of Formula Consider a circle of radius r Divide this circle into even number of equal parts . o r

12. . o r 2 8 6 5 4 1 7 3 AREA OF A CIRCLE Derivation of Formula Let us divide the circle into eight equal parts

13. . o r 2 8 6 5 4 1 7 3 3 2 1 6 5 4 8 7 AREA OF A CIRCLE Derivation of Formula Join these parts to form a parallelogram

14. Q. What is the circumference of a circle? . o r 2 8 6 5 4 1 7 3 Derivation of Formula C =  r C = 2  r C =  r 2 C = 2  r

15. Q. What is the area of a parallelogram? . o r 2 8 6 5 4 1 7 3 AREA OF A CIRCLE x Width x Width Length x Length Length x Width Length x Width

16. Area of parallelogram = length x Width Area of parallelogram =  r x r =  r 2 . o r 2 8 6 5 4 1 7 3 AREA OF A CIRCLE Derivation of Formula x

17. Hence area of circle = A  π r 2 . o r 2 8 6 5 4 1 7 3 AREA OF A CIRCLE x

18. We can divided the circle into a lot of sectors arrange them like this we will discover a rectangle the area of rectangle = length×width the area of the circle =   x x

19. EXAMPLES

20. AREA OF A CIRCLE What is the area of circle whose radius is 3 cm . Solution: area of the circle = π r 2 2 3.14 × = ………..  

21. Circle M is drawn inside a square of side length 14 cm and touched its sides . Calculate the area of the coloured part consider  =  

22. To find the area of coloured part we should first find the area of the square = side length × side length 14 × 14 = 196 c area of the circle = π r 2 = × = 154 c area of coloured part = 196 – 154 =42 c  

23. Find the area of each of the following (  = )  

24. A circle of circumference is 62.8 cm . Calculate its area (  = 3.14 )

25. Solution area of the circle = π r 2 circumference of the circle = π d d = = 20 cm r = 10 cm A = π r 2 3.14 × 100 = 314 c  

26. MR EMAD SAMY Thank you