Questionfloor?
34. Water is draining from a conical tank at a rate of $10 \pi$ cubic feet per minute. When full, the tank has a height of 16 feet and a radius of 10 feet. The tank is pointing point end down. How fast is the depth of the water changing when th? water is 8 feet deep? How fast is the water depth changing when the water is 4 feet deep?

Studdy Solution
Calculate $\frac{dh}{dt}$ when $h = 4$: $$\frac{dh}{dt} = \frac{-640}{25 \times 4^2} = \frac{-640}{400} = -1.6 \text{ feet per minute}$$
The rate at which the depth of the water is changing when the water is 8 feet deep is $-0.4$ feet per minute, and when the water is 4 feet deep is $-1.6$ feet per minute.