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Calculus

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Sand is poured onto a level piece of ground at the rate of 0.25 m^3/min and forms a conical pile whose height is equal to its base diameter. How fast is the height increasing at the instant when the height is 0.50 m? V = 1/3(pi)(r^2)h

I got 3/pie, is that correct?

  • Calculus -

    I got 4/π

    let the radius be r, then the height is 2r
    V= (1/3)πr^2 h
    = (1/3)πr^2(2r)
    = (2/3)πr^3
    dV/dt = 2π r^2 dr/dt
    when 2r=.5
    r = .25 and dV/dt = .25

    1/4 = 2π(1/16) dr/dt
    times 8
    2 = π dr/dt
    dr/dt = 2/π
    d(2r)/dt = d(height)/dt = 4/π

  • Calculus -

    Thank you!

  • Calculus -

    Where did you get 8 from?

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