A conical tank $($Figure $1),$ base diameter $D$ and height $H,$ is suspended in an inverted position to hold water. A leak at the apex of the cone causes water to leave with a mass flow rate of $c**\sqrt[\phantom{2}]{h},$ where $c$ is a constant and $h$ is the height of the water level from the leak at the bottom.

Determine the rate of change of height $h.$

$\frac{4c{H}^2}{D^2{h}^{\frac{3}{2}}}$

$-\frac{D^2{h}^2}{4H^2}$

$-\frac{4c{H}^2}{D^2{h}^{\frac{3}{2}}}$

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Part B

Express $h$ as a function of time $t$ and other known constants, $($constant density of water$),D,H,$ and $c$ if the tank were completely full at $t=0.$

$-\frac{4c{H}^2}{D^2{h}^{\frac{3}{2}}}$

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