Chapter 5, Problem 17P

You are designing a spherical tank (Fig. P5.17) to hold water for a small village in a developing country. The volume of liquid it can hold can be computed as

$V=\pi h^2\frac{\left[3R-h\right]}{3}$

where $V=$ volume $\left({\text{m}}^3\right),h=$ depth of water in tank $\left(\text{m}\right)$, and $R=$ the tank radius $\left(\text{m}\right)$.

FIGURE P5.17

If $R=3$ m, to what depth must the tank be filled so that it holds $30{\text{m}}^3$? Use three iterations of the false-position method to determine your answer. Determine the approximate relative error after each iteration. Employ initial guesses of 0 and R.