7 An oil slick is circular with radius \(r \mathrm {~km}\) and area \(A \mathrm {~km} ^ { 2 }\). The radius increases with time at a rate given by \(\frac { \mathrm { d } r } { \mathrm {~d} t } = 0.5\), in kilometres per hour.

1. Show that \(\frac { \mathrm { dA } } { \mathrm { d } t } = \pi r\).
2. Find the rate of increase of the area of the slick at a time when the radius is 6 km .