Question

a swimming pool is 5m wide, 10m long, 1m deep at the shallow end, and 3 m deep at its deepest point. a cross section is shown in the figure. if the pool is being filled at a rate of 0.1 m3/min, how fast is the water level rising when the depth at the deepest point is 1m?

Answer 1

When the water is y meters deep, the surface has a length of 5y and a width of 5. So, its volume is

v(y) = 25/2 y^2
dv/dt = 25y dy/dt

Now plug in y=1 and dv/dt=0.1 to find dy/dt