 Hi and welcome to the session. Let's work out the following question. The question says a balloon which always remains spherical is being inflated by pumping in gas at the rate of 900 centimeter cube per second. Find the rate at which the radius of the balloon is increasing when radius of balloon is 15 centimeter. So let's start with the solution to this question. Let R be the radius of spherical balloon and let V be its volume. Now volume of a sphere is given by 4 by 3 pi R cube. Now differentiating both the sides with respect to T, we have dV by dt is equal to 4 by 3 into pi R square into 3 into dr by dt. 3 gets cancelled with 3 and we have dV by dt is given to be 900. So we have 900 is equal to 4 pi R square into dr by dt. This implies dr by dt is equal to 900 divided by 4 pi R square that is equal to 225 divided by pi R square. Now this implies that dr by dt at R equal to 15 centimeter is equal to 225 divided by pi into 15 square. This implies that dr by dt is equal to 225 divided by 225 pi. 225 gets cancelled with this and therefore dr by dt that is the rate at which radius of the balloon is increasing is equal to 1 by pi centimeter per second. So our answer to this question is 7 by 22 centimeter per second because pi is approximately equal to 22 by 7. This is our answer to this question. I hope that you understood the solution and enjoyed the session. Have a good time.