Question

A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of change of the depth of the water when the water is 8 feet deep.

Answer 1

hey

Answer 2

I like to do this problem, but let me get something to eat okay, dont leave.

Answer 3

okay so you know dv/dt = 10
now by chain rule
\[\frac{dv}{dt}=\frac {dv}{dh} \frac{dh}{dt}\]
therefore
\[\frac{dh}{dt}=\frac{\frac{dv}{dt}}{\frac{dv}{dh}}\]

Answer 4

We can see
\[\frac{dv}{dh}_{,h=8}\]