Binomial Theory of Errors

[sineadb]

Hello! Can anyone help with this problem - I understand the binomial theory but am unsure whether my method is correct... The question is:

'The volume dimensions for a hemi-circular concrete wall are measured incorrectly during the setting out procedure. The external radius R is measure 5% more, the internal radius r is measured 3% less and the height H is measured 2% more than the original dimensions. Estimate the percentage change in the volume of the wall using binomial theory of errors.'

So for the volume of concrete the equation would be (piR^2)H/2 - (pir^2)H/2 for (external area x height) subtract (internal area x height), both divided by 2 as the wall is a hemi-circle.

Therefore using the theory I worked out the percentage for R using (1+0.05)^2*1.02 = 1.125 so 12.5% increase

For r (3% decrease) this would be (1-0.03)^2*1.02 = 0.960 so 4% decrease. I then added these two percentage change values to give 16.5% increase... Is this the correct method?


But then I wondered, as decreasing internal radius is effectively increasing the volume, would you use (1+0.03)^2 x 1.02 = 1.08? so 8% change?

Think I've just got a bit mixed up with it all now. If anyone could clarify I'd really appreciate it! Thanks, Sinead

 

[sineadb]

Bump!Anyone?

 

[JeffM]

Bump!Anyone?

Part of my problem is that I have no clue what the "binomial theory of error" is? It may be a Briticism that those of us who speak American English simply do not understand. Or it may be engineering jargon.

In any case, what is the relevance of your formulas to the volume of spheres? It looks as though you are dealing with cylinders.

EDIT: After doing a little research on the web, there is a binomial method of calculating confidence intervals. And there is a binomial approximation. Are you talking about one of those? If so, which one?