## Uncertainty questions???

When I am finding an area of a square with an uncertainty it’s obvious I do A=lw then Au=A[(lu/l)+(wu/w)). If I am doing the same with a cube, does the same logic apply? Vu=V[(lu/l)+(wu/w)+(hu/h)]. This is where lu is uncertainty of length, wu is uncertainty of width, and h is uncertainty of height. I’m thinking if the same applies with cube then rectangular prism should be straightforward.

Where I am stuck on is cylinder. Let’s say the radius is 10.0cm and the height is 30cm. How exactly would I find the uncertainty of a cylinder?

## Answer ( 1 )

The error formula comes from using differentials to estimate the error.

For a rectangle:

A=lw

dA = l*dw + w * dl

Factor out the lw

dA = lw(dw/w + dl/l) = A(dw/w + dl/l)

For a rectangular prism:

V = lwh = l(wh)

dV = l * d(wh) + wh*dl

dV = l * (w*dh + h*dw) + wh*dl

dV = lw*dh + lh*dw + wh*dl

Factor out lwh and you are left with

dV = lwh (dh/h + dw/w + dl/l) = dV = V (dh/h + dw/w + dl/l)

For a cube:

V = x^3

dV = 3x^2 dx

dV = V( 3dx/x)

Which is the same formula as the prism when l = w = h.