The volume V of a cylinder of height h and radius r is given by the expression V = πr2h. In a particular experiment, r is to be determined from measurements of V and h. The uncertainties in V and in h are :V ±7%, h ± 3%. Why this is 5% not 10%?
The volume V of a cylinder of height h and radius r is given by the expression V = πr2h. In a particular experiment, r is to be determined from measurements of V and h. The uncertainties in V and in h are :V ±7%, h ± 3%. Why this is 5% not 10%?
Hello there,
If we rearrange the equation, we find that . . .
[br][br]r=πhV[br][br]
. . . or alternatively . . .
[br][br]r=(πhV)21[br][br]
This implies that the percentage uncertainty, p(Δr), of the radius can be calculated by . . .
[br][br]p(Δr)=21[p(ΔV)+p(Δh)][br][br]
. . . since the percentage uncertainty within the parentheses is multiplied by the exponent. Therefore . . .