 Hello and welcome to this session. Let us understand the following question which says the radius of a circle is increasing uniformly at the rate of 3 cm per second. Find the rate at which the area of the circle is increasing when the radius is 10 cm. Now let us proceed on to the solution. Let the radius of the circle be denoted by r and area of the circle be denoted by a. It is given to us is that radius of a circle is increasing at the rate of 3 cm per second. That is dr by dt is equal to 3 and we have to find the rate at which the area of the circle is increasing. So area of a circle is given by pi r square. Now differentiating it with respect to t, so we get da by dt is equal to 2 pi r d by dt of r by chain rule. This implies da by dt is equal to 2 pi r dr by dt. Now dr by dt is given to us as 3 so this implies da by dt is equal to 2 pi r multiplied by 3 which is equal to 6 pi r. Now we have to find the value of da by dt when radius is equal to 10 cm. Therefore da by dt at r is equal to 10 is equal to 6 pi multiplied by 10 which is equal to 60 pi cm2 per second. Hence area is increasing at the rate of 60 pi cm2 per second when r is equal to 10 cm and this is our required answer. I hope you understood the question. Bye and have a nice day.