The total surface area of a closed cylindrical tank is 153.94 square meter. If the volume is to be maximum, what is its height in meters.

For maximum volume of a closed (both ends) cylinder of given surface area, or minimum surface area for given volume:
 

 

Total surface area:
$A = 2( \frac{1}{4}\pi d^2) + \pi d h$

$153.94 = \frac{1}{2}\pi h^2 + \pi h^2$

$\frac{3}{2}\pi h^2 = 153.94$

$h = 5.72 ~ \text{m}$