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15 July, 09:18

A cylindrical bucket is being filled with paint at a rate of 6 cm per minute. How fast is the level rising when the bucket starts to overflow? The bucket has a radius of 30 cm and a height of 60 cm.

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  1. 15 July, 09:40
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    Q: A cylindrical bucket is being filled with paint at a rate of 6 cubic cm per minute. How fast is the level rising when the bucket starts to overflow? The bucket has a radius of 30 cm and a height of 60 cm.

    Answer:

    0.00212 cm/min

    Step-by-step explanation:

    Volume of a cylinder

    V = πr²h ... Equation 1

    Where r = radius of the cylinder, h = height of the cylinder, π = pie.

    From Chain Rule

    dV/dt = (dV/dh) * (dh/dt) ... Equation 2

    Differentiating equation 1 with respect to h

    dVdh = πr² ... Equation 3

    Given: r = 30 cm, π = 3.14

    Substitute into equation 3

    dV/dh = 3.14 (30) ²

    dV/dh = 2826 cm²

    But, dV/dt = 6 cm³/min.

    Also substituting into equation 2

    6 (cm³/min) = 2826 (cm²) * dh/dt

    Making dh/dt the subject of the equation

    dh/dt = 6 (cm³/min) / 2826 (cm²)

    dh/dt = 0.00212 cm/min.

    Thus the level is rising at 0.00212 cm/min
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