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Math Help - sand problem

  1. #1
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    sand problem

    ok sand pouring from a chute forms a conical pile whose height is always equal to the diameter. if the height increases at a constant rate of 5 ft/min, at what rate is sand pouring from the chute when the pile is 10ft high? thanks in advance.
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  2. #2
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    Quote Originally Posted by slapmaxwell1 View Post
    ok sand pouring from a chute forms a conical pile whose height is always equal to the diameter. if the height increases at a constant rate of 5 ft/min, at what rate is sand pouring from the chute when the pile is 10ft high? thanks in advance.
    V = \frac{\pi}{3} r^2 h

    since h = 2r ... r = \frac{h}{2}

    V = \frac{\pi}{3} \left(\frac{h}{2}\right)^2 h

    simplify the formula for V in terms of h , then take the derivative w/r to time.

    you were given \frac{dh}{dt} = 5 ft/min ... calculate \frac{dV}{dt} when h = 10 ft
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