Answer:
[tex]\frac{dh}{dt}=\frac{3}{\pi r^{2}}[/tex] meters per minute
Step-by-step explanation:
Volume of a cylinder is given by the formula,
V = πr²h
Where r = radius of the cylindrical tank
h = height of the tank
Water is filling in this tank = 3 cubic meters per second
Derivative of volume will show the change in volume of the water in the tank.
[tex]\frac{dV}{dt}=\frac{d}{dt}(\pi r^{2}h)[/tex]
[tex]\frac{dV}{dt}=(\pi r^{2}) \frac{dh}{dt}[/tex]
By putting [tex]\frac{dV}{dt}=3[/tex] in the expression,
[tex]3=(\pi r^{2}) \frac{dh}{dt}[/tex] [Since 'r' is a constant]
[tex]\frac{dh}{dt}=\frac{3}{\pi r^{2}}[/tex]
Therefore, rate of increase in height of the water level will be represented by,
[tex]\frac{dh}{dt}=\frac{3}{\pi r^{2}}[/tex] meters per minute
