Determine how fast the length of an edge of a cube is changing at the moment when the length of the edge is 5cm and the volume of the edge i

Question

Determine how fast the length of an edge of a cube is changing at the moment when the length of the edge is 5cm and the volume of the edge is decreasing at the rate of 100cm^3/sec​

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Ladonna 4 years 2021-07-18T21:58:44+00:00 1 Answers 7 views 0

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  1. Sapo1
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    2021-07-18T22:00:21+00:00
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    Answer:

    1.333 cm/s

    Explanation:

    The formula for the volume of the cube V in term of its edge s is:

    V = s^3

    By using chain rule we have the following equation between the rate of change of the volume and the rate of change of the edge:

    \frac{dV}{dt} = \frac{dV}{ds}\frac{ds}{dt}

    100 = \frac{d(s^3)}{ds}\frac{ds}{dt}

    100 = 3s^2\frac{ds}{dt}

    \frac{ds}{dt} = \frac{100}{3s^2}

    We can substitute s = 5 cm:

    \frac{ds}{dt} = \frac{100}{3*5^2} = 100 / 75 = 1.333 cm/s

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