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

To measure $1L$ of water within the required error, we need to measure $h$ within the range of $[87.535mm,89.304mm]$.
$$V=36\pi h$$ To find how closely we must measure $h$ to measure $1000cm^3$ of water with an error of no more than $10cm^3$, basically is to find an interval $[a, b]$ of $h$ values such that for all $h\in[a,b]$: $$|36\pi h-1000|\le10$$ $$-10\le36\pi h-1000\le10$$ $$990\le36\pi h\le1010$$ $$\frac{990}{36\pi}\le h\le\frac{1010}{36\pi}$$ $$8.7535cm\le h\le8.9304cm$$ $$87.535mm\le h\le89.304mm$$ Therefore, to measure $1L$ of water within the required error, we need to measure $h$ within the range of $[87.535mm,89.304mm]$.