# Calculus

posted by .

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.

• 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.

## Similar Questions

1. ### algebra

the cube root of the volume of a cube gives the length of one side of the cube. volume=343cm cubed a. find the side length of the cube shown b. find the area of each face of the cube i have no idea how to do this!
2. ### Calculus

An ice cube is melting such that the side of the cube is decreasing at the rate of 1/4 t^2 cm / min. It is given that the side of the cube is 8cm at the start of the experiment. Calculate the length of the side of the cube when t = …
3. ### Statistics

University Hospital has been concerned with the number of errors found in its billing statements to patients. An audit of 100 bills per week over the past twelve weeks revealed the following number of errors: Week Number of Errors …
4. ### physics

Why is there always a difference between the experimentally calcuated error for resistance, and the actual components tolerance value?

1. A person's belief that he or she needs a drug to feel good or function normally (1 point) addiction psychological dependence emphysema tolerance 2. A large, dome-shaped muscle below the lungs (1 point) trachea alveoli diaphragm …
6. ### Language

Which of the following statements describe Jordan's view of the role of government in promoting tolerance ?
7. ### Health

A person who has physical craving or strong emotional need to use alcohol is showing signs of a- reverse tolerance ** b- tolerance c- rehabilitation d- addiction
8. ### statistics

A sample of blood is assayed for its alcohol content (BAC). The following BAC values are determined from six trials: 0.081%, 0.078%, 0.079%, 0.076%, 0.082%, 0.077% Assume the data follows a Gaussian distribution. For 84% of the possible …