The area \(A\) of a circle is given by \(A = \pi r^2\), where \(r\) is the radius.

To find the rate at which the area is increasing, we need \(\frac{dA}{dt}\).

Using the chain rule, \(\frac{dA}{dt} = \frac{dA}{dr} \times \frac{dr}{dt}\).

First, find \(\frac{dA}{dr}\):

\(\frac{dA}{dr} = \frac{d}{dr}(\pi r^2) = 2\pi r\).

Given \(\frac{dr}{dt} = 3\) m/h and \(r = 50\) m at midday, substitute these values:

\(\frac{dA}{dt} = 2\pi (50) \times 3 = 300\pi\).

Thus, \(\frac{dA}{dt} = 300\pi\) square metres per hour, or approximately 942 square metres per hour.