A water tank is in the shape of a right circular cone as shown above. The diameter of the cone is $10$ feet, and the height is $15$ feet. The shape of the water in the tank is conical with radius r feet and height h feet. At noon, water is leaking from the bottom of the tank at a rate of $12$ cubic feet per hour, and the volume of water in the tank is $27\backslash$pi cubic feet. At noon, what is the rate at which the height of the water in the tank is changing? $($The volume V of a right circular cone with radius r and height h is V$=1/3\backslash$pi r$^2$ h$)$

$($A$)$ Decreasing at $\frac{4}{9}$ feet per hour

$($B$)$ Increasing at $\frac{4}{9}$ feet per hour

$($C$)$ Increasing at $\frac{4}{3}$ feet per hour

$($D$)$ Decreasing at $\frac{4}{3}$ feet per hour