



 
Hi Veronica, Here is my diagram of the container at a time $t$ seconds. The length of $AB$ is 1 inch and the length of $BC$ is 5 inches. Let $h(t)$ be the length of $EC$ and $r(t)$ be the length of $DE,$ both in inches. These are both functions of time. The volume of a cone is \[V = \frac13 \pi \; r^2 h.\] Use the fact that triangles $ABC$ and $DEC$ are similar to find a relationship between $r(t)$ and $h(t)$ and then use this relationship to eliminate $r$ from the expression for the volume $V$ of the cone $DEC.$ The volume of the cone $DEC$ is a function of time and hence you can differentiate both sides of the new expression for the volume to obtain an equation with $V^\prime (t)$ on the left and an expression involving $h(t)$ and $h^\prime (t)$ on the right. Use the values of $h(t)$ and $h^\prime (t)$ when $h(t) = 1$ inch to find the value of $V^\prime (t)$ at this time. Penny  


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