A = пr^2
dA/dr = 2пr
You are given the rate of increase of surface area,
i.e. dA/dt = 30 km^2/day
The chain rule lets us write
dA/dt = (dA/dr)*(dr/dt)
i.e. dA/dt = (2пr)*(dr/dt) using dA/dr = 2пr
so, dA/dt = (10п)*(dr/dt) when r = 5 km
and 30 = (10п)*(dr/dt)
Finally dr/dt = 3/п = 0.95493 km/day