Answer:
The height of the water is increasing at a rate of 0.05m/min.
Step-by-step explanation:
Volume of a cylinder:
The volume of a cylinder, with radius r and height h, is given by:
[tex]V = \pi r^2h[/tex]
Radius 5 m
This means that [tex]r = 5[/tex], and so:
[tex]V = 25\pi h[/tex]
How fast is the height of the water increasing?
We have to differentiate V and h implictly in function of t. So
[tex]\frac{dV}{dt} = 25\pi\frac{dh}{dt}[/tex]
Being filled with water at a rate of 4 m3/min
This means that [tex]\frac{dV}{dt} = 4[/tex]. The questions asks [tex]\frac{dh}{dt}[/tex]. So
[tex]\frac{dV}{dt} = 25\pi\frac{dh}{dt}[/tex]
[tex]4 = 25\pi\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = \frac{4}{25\pi}[/tex]
[tex]\frac{dh}{dt} = 0.05[/tex]
The height of the water is increasing at a rate of 0.05m/min.
