The radius is 2/3 the height, so at a height of 2 ft, the radius of the surface is .. (2/3)*(2 ft) = 4/3 ft and the area of the surface is .. A = π*(4/3 ft)^2 = 16π/9 ft^2
The rate of change of height is the rate of change of volume divided by this number, .. dh/dt = (dV/dt)/A = (2 ft^3/min)/(16π/9 ft^2) = 18/(16π) ft/min .. ≈ 0.3581 ft/min
