A water tank has the shape of an upside-down cone with radius \( 2\text{m} \) and height \( 5\text{m} \) . The water is running out of the tank through a small hole at the bottom at a speed proportional to the square root of the depth of the water in the tank. Suppose that the water is running out at a rate of \( 3 \text{ m}^3/\text{min} \) when the depth of the water in the tank is \( 4\text{m} \) . Find the rate at which the water level is changing at this moment.
A \( 75/(54\pi) \)
B \( 75/(64\pi) \)
C \( 65/(54\pi) \)
D \( 65/(64\pi) \)
Solution
Correct Answer: Option B