 Hello and welcome to the session, let us understand the following question which says, find the rate of change of the area of a circle with respect to its radius r when a r is equal to 3 centimeter, b r is equal to 4 centimeter. Now before starting with the solution let us understand what do we mean by rate of change of quantities. If two quantities x and y are related to each other, satisfying the rule y is equal to f of x then dy by dx is called rate of change of y with respect to x. And the knowledge of this is the key idea towards this question. Now let us proceed on to the solution. The area a of a circle is given by pi r square. Now differentiating it with respect to r we get dA by dr is equal to 2 pi r. Therefore dA by dr at r is equal to 3 is equal to 2 pi multiplied by 3 which is equal to 6 pi and similarly dA by dr at r is equal to 4 is equal to 2 pi multiplied by 4 which is equal to 8 pi. Therefore for r is equal to 3 centimeter, area is increasing at the rate of 6 pi centimeter square per second and similarly for r is equal to 4 centimeter, area is increasing at the rate of 8 pi centimeter square per second which is the required answer. I hope you understood the question. Bye and have a nice day.