## University Calculus: Early Transcendentals (3rd Edition)

Greatest % error in height: $\frac{1}{3}$% of h
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=$\frac{dV}{V}=\frac{3\pi h^2dh}{\pi h^3}=3 \frac{dh}{h}$ $\frac{dh}{h}=\frac{1}{3}$%