2015 TWO(e)

A water container is constructed in the shape of a square-based pyramid. The height of the
pyramid is the same as the length of each side of its base.

A vertical height of 20 cm is then cut off the top of the pyramid, and a new flat top added.
The pyramid is then inverted and water is poured in at a rate of $3000{\text{ cm}}^3$ per minute.

Find the rate at which the surface area of the water is increasing when the depth of the water
is $15\text{ cm}$.

Volume of pyramid $=\frac{1}{3}\times$ base area $\times$ height

*You must use calculus and show any derivatives that you need to find when solving this problem.*