# So a cylindrical tank with a radius of 4ft fills with water at the rate of 20ft^3 sex

• Oct 21st 2007, 08:36 PM
Idontknow
So a cylindrical tank with a radius of 4ft fills with water at the rate of 20ft^3 sex
*seconds
Explain the volume of the tank as a function of the height. Express the depth of the water in the tank as a function of the time in t seconds.

I'm stuck on this problem in my homework, can you help me and explain it?
• Oct 21st 2007, 08:56 PM
Jhevon
Quote:

Originally Posted by Idontknow
*seconds
Explain the volume of the tank as a function of the height.

really not much to do here. we just want to manipulate the equations you already know.

For a cylinder,

$V = \pi r^2 h$

$\Rightarrow \boxed{h = \frac V{\pi r^2}}$

Quote:

Express the depth of the water in the tank as a function of the time in t seconds.
we know that $V = 20t$

(the volume of water increases by 20 ft^3 every second)

thus, $h = \frac {20t}{\pi r^2}$

$\Rightarrow \boxed{h = \frac {5t}{4 \pi}}$ ........since r = 4