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Math Help - Water level in a cone shaped tank using differentiation

  1. #1
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    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
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by simsima_1 View Post
    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
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