# Finding surface area with volume

ahmedb
Ok, so I did a test today for advance functions and there was a question: the volume of a pop can is 350ml, find the minimum surface area and determine the dimensions.
Where I got stuck:

350=pi(r)^2*h
h=350/pi(r)^2

SA= 2pi(r)^2+2pi(r)(h)
SA= 2pi(r)^2+2pi(r)(350/pi(r)^2)

=(2(pi(r)^3+350))/(pi(r))

I'm stuck here :S

Muphrid
How do I [STRIKE]shot web[/STRIKE] er, minimize function? Doesn't it have to do with the derivative having a certain value?

Hey ahmedb and welcome to the forums.

One thing you should be aware of is that volume is cubic metres (or centimetres or inches or some other unit of length) so you need to convert the liquid quantity to volume by looking at the density.

As Muphrid pointed out above, you want to look into finding a minimum which has a direct correspondence to the derivative being zero.

Nessdude14
This problem has nothing to do with density. You simply need to find the minimum value for the surface area function you came up with. To do this, you find the derivative of your SA function with respect to r, and set it to 0.

This problem has nothing to do with density. You simply need to find the minimum value for the surface area function you came up with. To do this, you find the derivative of your SA function with respect to r, and set it to 0.

If you want things in the right units, this is a critical step.

Mentor
ahmedb,
Homework problems should be posted in the Homework & Coursework section, not in the math technical section.

Homework Helper
Hey ahmedb and welcome to the forums.

One thing you should be aware of is that volume is cubic metres (or centimetres or inches or some other unit of length) so you need to convert the liquid quantity to volume by looking at the density.

As Muphrid pointed out above, you want to look into finding a minimum which has a direct correspondence to the derivative being zero.

This problem has nothing to do with density. You simply need to find the minimum value for the surface area function you came up with. To do this, you find the derivative of your SA function with respect to r, and set it to 0.

If you want things in the right units, this is a critical step.
No, it isn't. Liquid quantity is volume. Nothing in this problem has anything to do with density, weight, or mass.