Question

Given that V=[ð*D^2]*h/4
and
fractional error in W leading from the errors Äa, Äb and Äc from the measurement of a, b, and c is given by
ÄW/W= sqrt((nÄa/2)^2+(mÄb/2)^2+(pÄc/2)^2)
where one has a quantity W proportional to a^n* b^m* c^p,where a, b, and c are variables
calculate the ratio of the error in the volume to the mean volume (ÄV/V) in terms of the corresponding errors in the measurement of the diameter (ÄD) and the height (Äh)

Answer 1

If you use ISO-8859-1 encoding to send your text, it would be a little easier for us to understand your post.

As it is, many symbols are not obvious, although some are understandable.
(Ä)=δ
(ð)=π

Also, without a complete description of your problem, it is difficult to figure out what you need.

V=πD²h/4 is the volume of a cylinder. But it is not obvious where do the symbols W,m,n,p and a,b,c come from.

Answer 2

With MathMate's descriptions of symbols,

ln V = ln(pi/4) + 2ln D + lnh

Now take the differential of both sides.

äV/V = 2 äD/D + äh/h

If the measurement errors in D and h are random and uncorrelated, the rms error in the measured volume is

(äV/V)rms = sqrt[4(äD/D)^2 + (äh/h
)^2]

according to the root-sum-of-squares (RSS) rule.