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If the tolerance on the volume of a cube is a 2% error then what should the tolerance be fore each side?

So what i did was

dV = 3x^2 dx

dV/V = 2%

What should I do next? the answer is 2/3% but I don't know how it works.


  • Calculus -

    Let the three cube dimensions be w, l and h

    V = w l h

    dV/V = (lh dw + wh dl + wl dh)/(wlh)
    = dw/w + dl/l + dh/h = 2%

    If you apply the same relative tolerance to width, length and height, each should be 1/3 of 2%

    There is no reason that different tolerances could not be applied to different dimensions, however.

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