JPJC Applications of Differentiation Assignment 7 Q3

The surface area of a sphere of radius \(r\) metres is decreasing at a rate of \(0.4\)m\(^{2}\)s\(^{-1}\) at an instant when \(r=0.25\). Calculate the rates of decrease, at this instant, of the radius and the volume of the sphere.[4]

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