Answer
Greatest % error in height: $\frac{1}{3}$% of h
Work Step by Step
We need to find % error change in height: $\frac{dh}{h}$
% error change in volume = 1%
% error change=$\frac{change\ in\ dimension}{original\ dimension}$
$V=\pi h^3$
$dV=3\pi h^2 dh$
% error in volume=$\frac{dV}{V}=\frac{3\pi h^2dh}{\pi h^3}=3 \frac{dh}{h}$
$\frac{dh}{h}=\frac{1}{3}$%
