 Hello and welcome to the session. Let us understand the following question which says, a balloon which always remains spherical has a variable radius, find the rate at which its volume is increasing with the radius when the later is 10 cm. Now let us proceed on to the solution. Let R be the radius of the spherical balloon and V be the volume of the balloon. After find the rate at which the volume is increasing with the radius that is we have to find dV by dr. 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 sphere. Now differentiating it with respect to R because we have to find dV by dr, we get dV by dr is equal to 4 by 3 pi multiplied by 3 R square. 3 and 3 gets cancelled, so we are left with dV by dr is equal to 4 pi R square. Now we have to find dV by dr when radius is equal to 10 cm. Therefore it implies dV by dr at R is equal to 10 is equal to 4 pi multiplied by 10 multiplied by 10 which is equal to 400 pi. Hence required volume is increasing at the rate of 400 pi cm cube per second. When radius is 10 cm and this is the required answer, I hope you understood the question. Bye and have a nice day.