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CALCULUS

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Sand is being poured from a converyer belt forming a conical pile whose base diameter is eual to its height at all times. If the base diameter is inreasing at 2 m/min when the base is 2 m wide. How fast is the sand being poured onto the pile?

  • CALCULUS -

    given: 2r = h

    d(diameter)/dt = 2 m/min
    d(2r)/dt = 2 m/min
    d(r)/dt = 1 m/min

    V(ofcone) = (1/3)πr^2 h
    = (1/3)πr^2 (2r)
    = (2/3)π r^3

    dV/dt = 2πr^2 dr/dt
    = 2π(1^2)((1)

    = 2π m^3/min

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