DHS Tutorial Q3

A circular cylinder is expanding in such a way that. At time \(t\) seconds, the length of the cylinder is \(20x\) cm and the area of the cross-section is \(x\)cm\(^{2}\). Given that, when \(x=5\), the area of the cross-section is increasing at a rate of \(0.025\)cm\(^{2}\)s\(^{-1}\), find the rate of increase at this instant of

1. the length of the cylinder,[2]
2. the volume of the cylinder,[2]
3. the radius of the cylinder.[3]