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
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 $\Delta$ $$\frac{\Delta V}V=2\frac{\Delta D}D+\frac{\Delta H}H\implies \frac{\Delta D}D= ???$$