2021 NYJC P2 Q4

Air is pumped into a spherical elastic ball through a tiny hole at a constant rate of \(10\)cm\(^{3}\) per second. Assuming that the ball maintains a spherical shape throughout the process, find

1. the rate of increase of the radius of the ball at the instant when the radius is \(5\)cm,[2]
2. the rate of increase of the surface area of the ball at the instant when the radius of the ball is increasing at the rate of
   \(\frac{5}{72\pi }\)cm per second.[3]

[It is given that the surface area and volume of a sphere of radius \(r\) are \(4\pi {{r}^{2}}\) and \(\frac{4}{3}\pi {{r}^{3}}\) respectively.]