# How do you construct a 12-ounce cylindrical can with the least amount of material?

##### 1 Answer

I will do this only in metric units, but the idea will be clear.

Let's say we use

For the can (closed-topped) we need:

a top, a bottom and the outer surface.

Let's call **half** -diameter) of the can, and

Then the **volume** will be:

The **total surface area**

Top+bottom:

Side surface:

Total:

Since the volume is given, we can express

Differentiating, we get

This leads to:

**Answer** :

Diameter:

*Checking* the answer:

(close enough, with the rounding we've done)

**Remark** :

With the ounces and inches, you will have a lot of converting to do. I suggest you start by converting ounces to cubic inches.