# Math Help - Optimization-Open Topped Cylinder

1. ## Optimization-Open Topped Cylinder

This question is really bothering me help would be much appreciated

The cost per square meter of the sides of an open-topped cylindrical tank is twice the cost per square meter of the bottom. Find the most economical proportions for a tank of given volume.

2. Originally Posted by Calculus23
This question is really bothering me help would be much appreciated

The cost per square meter of the sides of an open-topped cylindrical tank is twice the cost per square meter of the bottom. Find the most economical proportions for a tank of given volume.
$V = \pi r^2 h$

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

$C = \pi r^2 + 2(2\pi r h)$

sub in the expression for h in terms of r in the cost equation to get C as a function of r, simplify, and find dC/dr to find the minimum cost.

remember that V is just a constant.

3. I am still confused... any more help?

4. Originally Posted by Calculus23
I am still confused... any more help?
I've told you exactly what to do.

1. substitute $\frac{V}{\pi r^2}$ in for $h$ in the cost equation.

2. simplify the cost equation.

3. take the derivative of the cost equation w/r to $r$ and minimize like you were taught in class.