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25 September, 00:40

Suppose a right circular cone has a fixed height 3.6 inches. Use differentials to estimate the change in the volume of the cone if its height is kept constant but its radius is decreased from 1.3 inches to 1.27 inches. Answer with both an exact value and rounded to 2 decimal places. approximate change in volume: ≈ (include units in your work)

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  1. 25 September, 00:59
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    dV/dt = 0,474552 in³/units of time

    dV/dt = 0,47 in³/units of time

    Step-by-step explanation:

    Volume for the right circular cone:

    V (c) = (1/3) * π*x²*h

    Where x is radius of the circular base, and h the heigt

    Differentiating on both sides of the equation, keeping in mind that h is constant, we get:

    dV/dt = (1/3) * 3,6*2*x*dx/dt (1)

    Now when radius changes from 1,3 to 1,27 inches or 0,03 in in/units of time

    dV/dt = (1/3) * 3,6 * 2 * (1,3) ²*dx/dt

    units h in inches

    radius in inches

    dx/dt in inches/units of time

    Then

    dV/dt = 0,474552 in³/units of time

    dV/dt = 0,47 in³/units of time
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