The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds, it becomes 7 units, then its radius after 9 seconds is

Step-by-step solution

Let surface area of the spherical balloon A = 4 π r 2 d A d t = 8 π r d r d t = k (let)       . . . 1 On integrating on both sides w.r.t t , we get 4 π r 2 = k t + C . Given that, at t = 0 ,   r = 3 . ⇒ 36 π = C Also given that, at t = 5 ,   r = 7 ⇒ 4 π × 49 = 5 k + 36 π ⇒ 5 k = 4 π 49 - 9 ⇒ 5 k = 4 π × 40 ⇒ k = 32 π On substituting k value in equation 1 we get, 4 π r 2 = 32 π t + 36 π &#8658