Asked by Nicole
                A machine starts dumping sand at the rate of 20 m3/min, forming a pile in the shape of a cone. The height of the pile is always twice the length of the base diameter. After 5 minutes, how fast is the base area of the base increasing?
 
I honestly have no idea how to start this question
            
        I honestly have no idea how to start this question
Answers
                    Answered by
            Reiny
            
    Since the height is twice the diameter, the height is equal to the radius of the circular base.
Let the radius be r
V = (1/3)π r^2 h, but h = r
V = (1/3) π r^3
dV/dt = π r^2 dr/dt
dr/dt = 20/(πr^2) **
when t = 5 min, V = 5(20) = 100 m^3
100 = (1/3)πr^3
300 = πr^3
r^3 = 300/π
r = (300/π)^(1/3) ***
area of base = A = πr^2
dA/dt = 2π r dr/dt
= 2π(***)(**)
= ......
I will let you do the button-pushing
    
Let the radius be r
V = (1/3)π r^2 h, but h = r
V = (1/3) π r^3
dV/dt = π r^2 dr/dt
dr/dt = 20/(πr^2) **
when t = 5 min, V = 5(20) = 100 m^3
100 = (1/3)πr^3
300 = πr^3
r^3 = 300/π
r = (300/π)^(1/3) ***
area of base = A = πr^2
dA/dt = 2π r dr/dt
= 2π(***)(**)
= ......
I will let you do the button-pushing
                    Answered by
            Steve
            
    huh? height is twice the diameter, not half h = 4r
Make that change, Nicole, and redo the steps.
    
Make that change, Nicole, and redo the steps.
                    Answered by
            Reiny
            
    thanks Steve
    
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