# Math Help - Cylindrical tank- not sure if pre-calc or algebra

1. ## Cylindrical tank- not sure if pre-calc or algebra

A Cylindrical tank 4 ft in diameter fills with water at the rate of 10 ft/s. Express the depth of the water in the tank as a function of the time t in seconds.Assume the tank is empty at time t=0.

2. ## Re: Cylindrical tank- not sure if pre-calc or algebra

Originally Posted by mikewezyk
A Cylindrical tank 4 ft in diameter fills with water at the rate of 10 ft/s. Express the depth of the water in the tank as a function of the time t in seconds.Assume the tank is empty at time t=0.
The volume of a cylindar is

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

The amount of water in the tank is

$V=10t$

Combining these gives

$h=\frac{10t}{4\pi }=\frac{5t}{2\pi}$