Question

SCALCET8 3.9.005.MI. A cylindrical tank with radius 5 m is being filled with water at a rate of 4 m3/min. How fast is the height of the water increasing

Answer 1

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:

$V = \pi r^2h$

Radius 5 m

This means that $r = 5$, and so:

$V = 25\pi h$

How fast is the height of the water increasing?

We have to differentiate V and h implictly in function of t. So

$\frac{dV}{dt} = 25\pi\frac{dh}{dt}$

Being filled with water at a rate of 4 m3/min

This means that $\frac{dV}{dt} = 4$. The questions asks $\frac{dh}{dt}$. So

$\frac{dV}{dt} = 25\pi\frac{dh}{dt}$

$4 = 25\pi\frac{dh}{dt}$

$\frac{dh}{dt} = \frac{4}{25\pi}$

$\frac{dh}{dt} = 0.05$

The height of the water is increasing at a rate of 0.05m/min.