Question

An inverted conical water tank with a height of 16 ft and a radius of 8 ft is drained through a hole in the vertex at a rate of 5 ft^3/s. What is the rate of change of the water depth when the water is 4 ft

Answer 1

using similar triangles, it is easy to see that when the water has depth y, the radius of the water surface is y/2

so, the volume of water is

v = pi/3 (y/2)^2 y = pi/12 y^3
now, use the fact that
dv/dt = pi/4 y^2 dy/dt
to find your answer.