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**[SOLVED] Optimization Problem**

**1. Homework Statement**

A tin can is to have a given capacity. Find the ratio of height to diameter if the amount of tin (total surface area) is a minimum.

**2. Homework Equations**

c=pi(r^2)h

surface area = 2pi(r^2)+2h(pi)r

**3. The Attempt at a Solution**

h= c/(pi(r^2))

surface area = 2pi(r^2)+2h(pi)r

= 2pi(r^2)+2pi(r)(c/(pi(r^2)))

= 2pi(r^2) + c(r^-1)

Now, derivate of surface area:

SA` = 4hr - c/(r^2)

0 = ( 4h(r^3)-c )/(r^2)

4h(r^3)=c

r = [tex]\sqrt[3]{c/(4pi)}[/tex]

After this I don't know what to do. Can someone please guide me? Thanks.