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Math Help - Calculate the side of the cube

  1. #1
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    Post Calculate the side of the cube

    The volume of a cube increases by 2.0 m^3 / s, With what speed does the cube's side changes when the side is 6.0 m?

    Thx for any help I can get here!
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  2. #2
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    Re: Calculate the side of the cube

    Quote Originally Posted by Aiyla View Post
    The volume of a cube increases by 2.0 m^3 / s, With what speed does the cube's side changes when the side is 6.0 m?

    Thx for any help I can get here!
    We are given dV/dt = 2.0 We want dL/dt (L is length of side) Use dL/dt = dV/dt*dL/dV V=L^3 dV/dL =3L^2 So dL/dV = 1/(3L^2)
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  3. #3
    Junior Member Sarasij's Avatar
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    Re: Calculate the side of the cube

    Quote Originally Posted by Aiyla View Post
    The volume of a cube increases by 2.0 m^3 / s, With what speed does the cube's side changes when the side is 6.0 m?

    Thx for any help I can get here!
    I hope you know basic calculus. I am answering your question with it.

    Let the volume and a side of a cube be V m3 & a m. respectively.

    So, V=a3

    Now differentiate both sides with respect to time t.

    i.e. dV/dt = 3a2da/dt

    We have to find da/dt while a=6 & we know dV/dt=2.

    i.e. 2 = 3 x 62 x da/dt.

    or, da/dt = 2/(3 x 36) = 1/54 m/s.
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  4. #4
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    Re: Calculate the side of the cube

    We know that V = L^3. Differentiating both sides with respect to time t,

    \frac{dV}{dt} = 3L^2 \frac{dL}{dt}

    Particularly, when \frac{dV}{dt} = 2 \frac{m^3}{s} and L = 6 m,

    \frac{dL}{dt} = \frac{1}{54} \frac{m}{s}
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