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26 August, 15:03

A water tank has the shape of an inverted circular cone with base radius 2m and height 4m. If water is being pumped into the tank at a rate of 2 m3 / min, find the rate at which the water level is rising when the water is 3 m deep.

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  1. 26 August, 18:14
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    The volume of the tank is a circular cone, therefore it is given by:

    V = πr²h/3

    V = volume, r = base radius, h = height or water level

    Differentiate both sides with respect to time t. The base radius r doesn't change over time so treat it as a constant:

    dV/dt = πr² (dh/dt) / 3

    Given values:

    dV/dt = 2m³/min

    r = 2m

    Plug in and solve for dh/dt:

    2 = π (2) ² (dh/dt) / 3

    dh/dt = 0.48m/min

    The water level is increasing at a rate of 0.48m/min
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