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Math Help - increasing surface area

  1. #1
    TGS
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    increasing surface area

    The volume of a cube is increasing at a rate of 10cm^3/min. How fast is the surface area increasing when the length of an edge is 10cm?

    I don't understand this question at all..
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by TGS View Post
    The volume of a cube is increasing at a rate of 10cm^3/min. How fast is the surface area increasing when the length of an edge is 10cm?

    I don't understand this question at all..
    V=a^3

    S=6a^2

    \frac{dV}{dt}=10cm^3/min

    3a^2\frac{da}{dt}=10

    3*10^2\frac{da}{dt}=10

    \frac{da}{dt}=\frac{1}{30}

    \frac{dS}{dt}=6*2a\frac{da}{dt}=12*10*\frac{1}{30}  =4cm^2/min

    So, the surface area is increasing at a rate of 4cm^2/min.
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