 Hello and welcome to the session, let us understand the following question which says a balloon which always remains spherical on inflation is being inflated by pumping in 900 cubic centimeters of gas per second, find the rate at which the radius of the balloon increases when the radius is 15 centimeter. Now let us proceed on to the solution. Let V be the volume of the spherical balloon. It is given to us that balloon is inflated by pumping in 900 cubic centimeters of gas per second, therefore it means dV by dt is equal to 900. Let R be the radius of the swell and here we have to find the rate at which the radius of the balloon increases. So it means we have to find dr by dt. We know volume of a sphere is given by V is equal to 4 by 3 pi R cube where R is the radius of the swell. On differentiating it with respect to T we get dV by dt is equal to 4 by 3 pi multiplied by 3 R square dr by dt. 3 and 3 gets cancelled so we get 4 pi R square dr by dt and on left hand side we have dV by dt. Now substituting the value of dV by dt as 900 we get 900 is equal to 4 pi R square dr by dt. This implies dr by dt is equal to 900 by 4 pi R square. 900 get cancelled by 4 and we get here 225 so it implies dr by dt is equal to 225 by pi R square. Now in the question we have to find dr by dt at radius 15 centimeter so dr by dt at R is equal to 15 is equal to 225 by pi multiplied by 15 multiplied by 15. This gets cut off with 225 and we get here 15 and again 15 and 15 gets cancelled so it is equal to 1 by pi. Hence radius of the balloon increases at the rate of 1 by pi centimeter per second which is the required answer. I hope you understood this question. Bye and have a nice day.