Question

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
V=x^3

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.

Thanks.

Answer 1

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.