Question

How fast is the water level rising when the water is 1 foot deep?

A cylindrical water trough has a diameter of 6 feet and a height of 2 feet. It is being filled at the rate of 4 ft^3/min. How fast is the water level rising when the water is 1 foot deep?

Answer 1

0.00707 [m/sec] (example metric system!)

Explanation:

I have no clue of the imperial system haha, but to give you an idea here is how you would do it using the metric system.
Say the water through has a diameter of 6 meter. Then for every meter the water is rising, a water volume is needed of
`V = 1*(6/2)^2 * pi = 9.425 ["m"^3] -> 9.425 ["m"^3/"m"]`

Say the water is added with a rate of:
`4 ["m"^3/min] = 4/60 ["m"^3/sec] = 1/15["m"^3/sec]`

Then the rate at which the water is rising is:
`(1/15["m"^3/sec])/(9.425 ["m"^3/"m"]) = 0.00707 ["m"/sec]`