Chapter 16, Problem 3P

Design the optimal cylindrical tank with dishedends (Fig. P16.3). The container is to hold $0.5m^3$ and has walls of negligible thickness. Note that the area and volume of each of the dished ends can be computed with

$A=\pi \left(h^2+r^2\right)V=\frac{\pi h\left(h^2+3r^2\right)}{6}$

(a) Design the tank so that its surface area is minimized. Interpret the result.

(b) Repeat part (a), but add the constraint $L\ge 2h$.

FIGURE P16.3