8 At time \(t\) seconds, the radius of a spherical balloon is \(r \mathrm {~cm}\). The balloon is being inflated so that the rate of increase of its radius is inversely proportional to the square root of its radius. When \(t = 5 , r = 9\) and, at this instant, the radius is increasing at \(1.08 \mathrm {~cm} \mathrm {~s} ^ { - 1 }\).

1. Write down a differential equation to model this situation, and solve it to express \(r\) in terms of \(t\).
2. How much air is in the balloon initially?
   [0pt] [The volume of a sphere is \(V = \frac { 4 } { 3 } \pi r ^ { 3 }\).]