A cube$-$shaped water tank having $7$ ft side lengths is being filled with water. The bottom is solid metal but the sides of the tank are thin glass which can only withstand a maximum force of $100$ lb$.$ How high $($in ft$)$ can the water reach before the sides shatter?

$($Assume a density of water $=62\mathrm{.}4$ lb$/$ft$3.$

Round your answer to two decimal places.$)$