(Solved): 9. (10pts.) An inverted conical water tank with a height of \( 12 \mathrm{ft} \) and a radius of \ ...

9. (10pts.) An inverted conical water tank with a height of \( 12 \mathrm{ft} \) and a radius of \( 6 \mathrm{ft} \) is drained through a hole in the vertex at a rate of \( 2 \mathrm{ft}^{3} / \mathrm{s} \). What is the rate of change of water depth when the water depth is \( 3 \mathrm{ft} \) ? (Hint: Use similar triangles. The volume of a right circular cone is \( V=\pi r^{2} h / 3 \) )