 Hello and welcome to the session. In this session, we will discuss the relationship between the circumference and area of a circle. First of all, let us realize what is the radius, diameter, circumference and area of a circle. First of all, let us discuss the radius of a circle. Now here you can see a circle with center O. Now a line segment from the center of a circle to a point on the circle is called radius of a circle and here is the radius of this circle. So here this is the line segment from the center of the circle to a point on the circle. So this is the radius of the given circle. Similarly all these line segments represent radius of this given circle. Now let us discuss diameter. Now any line segment whose n points are on the circle and passes through the center is called diameter of a circle. Now here you can see that a b is the diameter of the given circle as its n points a and v lie on the circle through the center O. Now let us denote the diameter by d and radius that is the line segment starting from the center to the point on the circle is denoted by r. Now we can see that length of diameter carries the radius that is d is equal to 2r we can say r is equal to d upon 2. Now let us discuss of a circle. Now circumference of a circle is the distance around the circle it is given by c which is equal to 2 by r where is a constant with value 22 by 7 and r is radius of a circle. We can also write circumference in terms of diameter. Now we know that diameter d is equal to 2r. So circumference c which is equal to 2 by r can be written as pi into 2r. Now here we know that d is equal to 2r so it is equal to pi into d. We have written in terms of diameter of a circle. Now let us discuss area of a circle. Now area is and area of a circle is given by 22 a is equal to pi r square where pi is a constant with value 22 by 7 and r is the radius of a circle. Now let us express area in terms of diameter. Now we know that diameter d is equal to 2r equal to d upon 2. Let us put this value of r in the formula of area which is a is equal to pi r square. Now r is equal to d upon 2 so it will be pi into d upon 2 whole square which implies is equal to m into d square by 4. And now let us derive relationship between area and circle. Now we know that of a circle is given by c is equal to 2 pi r or we can write c is equal to pi into d where pi is a constant and d is the diameter of a circle and this implies d is equal to c upon pi. Circle is given by a is equal to 1. In terms of diameter we can write a is equal to pi into d square by 4. Now let us see equation number one. Now putting d is equal to c upon 1 pi whole square this whole upon 4 which implies a is equal to upon pi square and this whole upon c square upon 4 pi. So this implies a is equal to c square upon 4 pi. Therefore area of a circle is equal to square of the circumference of a circle divided by 4 pi where pi is the constant with value 22 by 7 the relationship between area and circumference of a circle. So in this session we have learned the relationship between area and circumference of a circle and this completes our session. Hope you will have enjoyed this session.