Thread: Water level in a cone shaped tank using differentiation

Model a water tank by a cone 40ft hight with a circular base of radius 20ft at the top. Water is flowing into the tank at a constant rate of 80ft^3/min. How fast is the water level rising when the water is 12ft deep? Answer should be in the nearest hundredth of a foot per min.

Question 1: am i solving for dV/dt or dh/dt
Question 2: if you start with V=(1/3)pi*r^2h does that mean that r (radius) and h (height) are already given?
Question 3: if i'm solving for dh/dt then what/how do i find what dV/dt is to begin with

Originally Posted by simsima_1

Model a water tank by a cone 40ft hight with a circular base of radius 20ft at the top. Water is flowing into the tank at a constant rate of 80ft^3/min. How fast is the water level rising when the water is 12ft deep? Answer should be in the nearest hundredth of a foot per min.

Question 1: am i solving for dV/dt or dh/dt

you are solving for dh/dt (dV/dt is given, there is no need to solve for it)

Question 2: if you start with V=(1/3)pi*r^2h does that mean that r (radius) and h (height) are already given?

not necessarily. the radius is given, but get rid of it. solve for r in terms of h (similar triangles is usually the best way to do this) then replace r in the formula with the function of h so you have the volume as a function of the height only, then differentiate implicitly, the only unknown will be dh/dt, solve for it.

Question 3: if i'm solving for dh/dt then what/how do i find what dV/dt is to begin with

dV/dt is given. read the question again, it is 80 ft^3/min