Calculus(answer needed immediatly,thanks)

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A paper cup has the shape of a cone with height 8cm and radius 3cm at the top. Water is being poured into the cup at the rate of 2cm3/s. How fast is the water level rising when the water is 6cm deep?

  • Calculus(answer needed immediatly,thanks) -

    1. Express r in terms of h:
    r=3/8h
    2. Express volume in terms of h:
    V=(1/3)πr²h
    =(1/3)π(3h/8)²h
    =(3π/64)h³
    dV/dh=(9π/64)h²
    dV/dt=2 cm³s-1

    dh/dt
    =(dV/dt)/(dV/dh)
    =2*64/(9πh²)
    =128/(9πh²)
    =0.1257 cm-s-1

  • Calculus(answer needed immediatly,thanks) -

    thank you .

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