Answer:
Thus, the depth of water is rising at a rate of [tex]\frac{5}{16\pi}\text{ meter per minute}[/tex].
Step-by-step explanation:
We are given the following in the question:
Diameter of cylindrical tank = 8 m
Radius of tank = 4 m
Water is flowing into a vertical cylindrical tank at the rate of 5 cubic meter per minute.
We have to find the rate at which the depth of the water is rising.
Volume of cylindrical tank =
[tex]V = \pi r^2 h\\\text{where r is the radius of tank and h is the height of the tank.}[/tex]
Putting the values, we get:
[tex]V = \pi (4)^2 h = 16\pi h[/tex]
Differentiating with respect to time, we get:
[tex]\displaystyle\frac{dV}{dt} = 16\pi\frac{dh}{dt}[/tex]
Putting the values, we get:
[tex]5 = 16\pi \displaystyle\frac{dh}{dt}\\\\\frac{dh}{dt} = \frac{5}{16\pi}\text{ meter per minute}[/tex]
Thus, the depth of water is rising at a rate of [tex]\frac{5}{16\pi}\text{ meter per minute}[/tex].
