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

1. ## 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?

2. 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,

$\displaystyle V = \pi r^2 h$

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

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

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

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

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