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Apr 2808:00 AM PDT
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10 Feb 2023, 18:52
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Pmar2012
Bunuel IanStewart Pmar2012 KarishmaB : I like this methodology
However - i dont see why we are SUMMING UP the deviations.
We should be MULTIPLYING the deviations instead
Why ? Because it is 200 x 200 x 300
Thus the deviations are (0.5 %) x (0.5 %) x (0.3333 %)
Thoughts ?
10 Feb 2023, 21:24
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jabhatta2
It's true that when we increase the dimensions by 0.5%, 0.5% and 0.3333...% we're really multiplying the volume by 1.005*1.005*1.00333333.... (you need to add 100% or 1 to each percentage in the part of your post I've highlighted to get the right percent increase). But when we have three very tiny percent increases, we can approximate the change just by adding them, because the compounding effect will be nearly zero. If you make an investment, say, and it increases in value by 1% each year for three years, you'll make just very slightly more than 3% (what you get by adding 1% + 1% + 1%), because there's almost no compounding with a percent change that small, unless you compound many, many times. I'm essentially just repeating what ThatDudeKnows' said above in his post. So as an approximation, it's fine just to add here. If the percent changes were large, however -- if we were increasing each dimension by 30%, say -- then there would be meaningful compounding, and adding would no longer give us a good estimate (the volume would increase in this case by roughly 120%, not by the 90% you'd get by adding 30 three times).
11 Feb 2023, 01:21
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jabhatta2
Though Ian has already explained it, all I would like to say is try out the calculations to see it yourself too.
New Volume = LBH*(1 + 0.5%)(1 + 0.5%)(1 + 0.33%)
We need to get the value of the highlighted. Say the percentages are a, b and c for ease.
(1 + a)(1 + b)(1 + c) = 1 + a + b + c + ab + bc + ca + abc
Since a, b and c are very small values (0.5% etc), ab becomes much smaller .0025% which is much much smaller than a, b and c and hence can be ignored. Obviously abc is even smaller so can be ignored too.
New Volume = LBH* (1 + 0.5% + 0.5% + 0.33%) = LBH * (1 + 1.33%) = LBH + LBH * 1.33% approximately
So the change in volume is approximately LBH * 1.33%.
