Need help with this related rates problem?

Question

anonymous · Answer

A cylindrical swimming pool (whose center axis is vertical) is being filled from a fire hose at a rate of 5 cubic feet per second. If the pool is 40 feet across, how fast is the water level increasing when the pool is one third full?
12 hours ago

campbell_st · Answer

well you know the rate of change in the volume with respect to time

$$\frac{dV}{dt} = 5$$

you know the volume of the cylinder

$$V = \pi r^2 h$$

then rewriting the equation with h as the subject 

$$h = \frac{V}{2 \pi r^2}$$

so then the rate of change in height with respect to time should be 

$$\frac{dh}{dt} = \frac{dh}{dV} \times \frac{dV}{dt}$$

and thinking about the problem... I think its a constant rate of change