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.

To find the tolerance for each side of the cube, you need to solve for dx (the change in the length of each side). Let's continue from the point where you have dV/V = 2%.

You have the equation dV = 3x^2 dx. Now, substitute dV/V with 2% or 0.02:

0.02 = 3x^2 dx.

Next, solve this equation for dx, the change in the length of each side. To do this, divide both sides of the equation by 3x^2:

0.02/(3x^2) = dx.

Simplifying further, we get:

0.00667/x^2 = dx.

This represents the change in each side length (dx) required to achieve a 2% error in volume (dV). However, the question is asking for the tolerance, which is generally represented as a percentage. To convert this change in length to a percentage, divide dx by x and multiply by 100:

(0.00667/x^2) * (1/x) * 100 = (0.00667/x^3) * 100 = 0.00667/x^3 * 100%.

Simplifying further, we get:

0.66/x^3.

Therefore, the tolerance for each side of the cube is 0.66/x^3%.

Note: Make sure to substitute x with the actual value of the side length in order to find the specific tolerance for that cube.

To find the tolerance for each side of the cube, let's first solve for dx in terms of the tolerance:

dV/V = 2%

dV = (3x^2) dx

Substituting the values, we have:

2% = (3x^2) dx

Now, we want to isolate dx:

dx = (2%)/(3x^2)

The question asks for the tolerance on each side, which can be represented as dS. Since the cube has all sides equal, we have:

dS = dx

Therefore, the tolerance for each side of the cube should be:

dS = (2%)/(3x^2)

Notice that this equation depends on the value of x, which represents the length of each side of the cube.

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.