Question 1193216
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The volume of the cone is {{{(1/3)(pi)(r^2)h}}}<br>
We are given dV/dt; we need to determine dh/dt.  So we need to express the volume as a function of h only.<br>
The full cone has height 6 and diameter 3, so its radius is 1.5.  Since the sides of the cone are straight, the radius is always 1/4 of the height.<br>
{{{r=h/4}}}
{{{V=(1/3)(pi)(r^2)h=(1/3)(pi)(h^2/16)h=(1/48)(pi)h^3}}}<br>
{{{15=dV/dt=(dV/dh)(dh/dt)=((1/16)(pi)h^2)(dh/dt)}}}<br>
{{{dh/dt=240/((pi)h^2)}}}<br>
At the moment the cone is filled, the height h is 6, and<br>
{{{dh/dt=240/(36pi)=20/(3pi)}}}<br>
ANSWER: Just as the tank is filled, the water is rising at a rate of {{{20/(3pi)}}} cm/sec<br>