Linearization to estimate uncertainty

Question

Consider a cone of height H and diameter D

Use linearization to estimate the allowable percentage error in the measurement of D if the colume of the cone is to be determined to within 2% of its true value?

So I know you are supposed to differentiate the volume of a cone, but by what and why? Thanks

score 0 · Answer 1 · answered Sep 22 '19 at 08:01

0

For a right circular cone, the volume is given by$$V=\frac \pi {12}D^2H$$ Use logarithmic differentiation to get $$\frac{dV}V=2\frac{dD}D+\frac{dH}H$$ Going from the $d$'s to $\Delta$ $$\frac{\Delta V}V=2\frac{\Delta D}D+\frac{\Delta H}H\implies \frac{\Delta D}D= ???$$

answered Sep 22 '19 at 08:01

Claude Leibovici

260,315

Hi, but how will I know the value of $\frac{\Delta H}H$ ? – Jisbon Sep 22 '19 at 12:47
May be, no error on $H$. – Claude Leibovici Sep 22 '19 at 15:33
So the answer is 4%? – Jisbon Sep 23 '19 at 05:01

Linearization to estimate uncertainty

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