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Thread: related rates prob: how fast is the surface area increasing?

  1. #1

    related rates prob: how fast is the surface area increasing?

    I am doing a related rates problem and I have no idea how to set it up. I haven't been able to find any examples in my book, notes or web on this one. I need help setting this up.

    "The volume of a cube is increasing at a rate of 10cm^3 per minute. How fast is the surface area increasing when the length of an edge is 30 cm."

    Any help as soon as possible would greatly be appreciated.
    Jessica

  2. #2
    Senior Member skeeter's Avatar
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    The volume of a cube is increasing at a rate of 10cm^3 per minute
    dV/dt = 10 cm<sup>3</sup>/min

    How fast is the surface area increasing when the length of an edge is 30 cm.?
    they want dA/dt when s = 30 cm

    equations needed ...
    volume of a cube, V = s<sup>3</sup>
    surface area of a cube, A = 6s<sup>2</sup>

    d/dt[A = 6s<sup>2</sup>]
    dA/dt = 12s(ds/st)
    to find dA/dt ... you have s, but need the value of ds/dt.

    d/dt[V = s<sup>3</sup>]
    dV/dt = 3s<sup>2</sup>(ds/dt)
    you have dV/dt and s ... you can solve for ds/dt, then you can determine dA/dt.

  3. #3
    thanks that really helps! I am so glad you replied quickly.
    Jessica

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