# Volumes

• May 24th 2010, 07:28 PM
name101
Volumes
Hello,

I am stumped on this question. I think I'm missing something really obvious but here is goes.

"You have been asked to design a 1000cm^3 can shaped like a right cylinder. What dimensions will use the least material?"

So I have V = $\displaystyle \pi r^2h$
Which is given for obvious reasons. But I really don't know how to go from there.
If I get the derivative of the formula I will have 2 variables and then I start to confuse myself.
• May 24th 2010, 07:44 PM
Diemo
The amount of material used would be the surface area. You want to minimise the amount of material used. (I.e. Set the derivative of the area equal to zero. I think it has to be the derivative with respect to the radius, because with respect to the height I get r=0 and h=infinity). This will give a relationship between your radius and your height. Put this into your equation for volume and viola...
• May 24th 2010, 08:55 PM
drumist
You know that

$\displaystyle V=\pi r^2 h=1000$

Solving for $\displaystyle h$ gives

$\displaystyle h=\frac{1000}{\pi r^2}$

Determine an equation for surface area of the cylinder, then use the above equation to eliminate $\displaystyle h$ from the equation. You will be left with only one variable.
• May 26th 2010, 07:41 PM
name101
Cheers for that :D, I got it working now :P