2018 TWO(e)

A water tank is in the shape of an inverted right-circular cone.

The height of the cone is 200 cm and the radius of the cone is 80 cm.

The tank is being filled with water at a rate of $150{\mathrm{cm}}^3$ per second.

At what rate will the surface area of the water in the tank be increasing when the depth of
water in the tank is 125 cm?

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