calculus

Sand is poured at the rate of 10 m cube /min so as to form a conical pile whose altitude is always equal to the radius of its base

a) How fast is the radius increasing when it is 5 meters?
b) Find the rate at which the area of its base is increasing when the radius is 5m

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  1. So in V = (1/3)π r^2 h, the value of h = r, so we get
    V = (1/3)π r^3

    dV/dt = π r^2 dr/dt

    a) plug in dV/dt = 10 m^3 and r = 5m, then solve for dr/dt

    b) Area of base = πr^2
    dA/dt = 2πr dr/dt
    you have dr/dt from a) and r = 5

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    Reiny
  2. so sir reiny the answer i got in your solution is
    a.0.4 m/min
    b.4 m/min
    that is right?

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  3. no ....

    dV/dt = π r^2 dr/dt
    10 = π(25)dr/dt
    dr/dt = 10/(25π) = .127...

    which of course means your second answer is also incorrect
    dA/dt = 2πr dr/dt
    = 2π(5)(.127...) = 4

    You also had 4, but should not have obtained that answer if you used
    the wrong answer to a)

    very strange

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    Reiny

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