A conical tank has height 3 m and radius 2 m at the top. Water flows in at a rate of 1.4 \text{m}^3\text{/min}. How fast is the water level rising when it is 2.6 m?

Answer 1

Oh, it is pointed at the bottom?

area = pi r^2

radius = (1/3) h for 1 at the top and 0 at the bottom
so surface area A = pi (1/9)h^2
for h = 2.6, A = 2.36 meters^2

d V = A dh
dV/dt = A dh/dt or dh/dt = (1/A)dV/dt
dV/dt given as 1.4 m^3/min
so
dh/dt = 1.4/2.36 = .593 m/min