From the given question
The volume of a cone is:
[tex]V=\frac{1}{3}\times\pi\times r^3[/tex]
Now,
We are given with radius and the height of the cone
So,
We can solve for the radius as a function of water level using ratio and proportion
Then,
[tex]\begin{gathered} \frac{3}{9}=\frac{r}{h} \\ r=\frac{h}{3} \end{gathered}[/tex]
Substitute the value of r into the above formula
So,
[tex]\begin{gathered} V=\frac{1}{3}\times\pi\times r^3 \\ V=\frac{1}{3}\times\pi\times(\frac{h}{3})^3 \\ V=\frac{h^3}{81}\times\pi \end{gathered}[/tex]
Then,
Taking derivatives
[tex]\begin{gathered} V=\frac{h^3}{81}\times\pi \\ \frac{dV}{dt}=\frac{h^3}{81}\times\pi \end{gathered}[/tex]
The,
Solving for the dh/dt
So,
[tex]\begin{gathered} \frac{dV}{dt}=10\text{ and h=3, then } \\ \frac{dh}{dt}=9.55m\text{ /s} \end{gathered}[/tex]
Hence, the answer is 9.55.
