(Solved):   You have been asked to design a 1-Liter can shaped like a right circular cylinder. What di ...

 

You have been asked to design a 1-Liter can shaped like a right circular cylinder. What dimensions will use the least material? (i.e. Find the \( r \) and \( \mathrm{h} \) that minimizes the surface area of the can). Use the following facts. \( 1 \mathrm{~L}=1000 \mathrm{~cm}^{3} \) (that is the volume) \( \mathrm{V}=\pi r^{2} h \quad \) (Surface area) \( \rightarrow \quad \mathrm{S}=2 \pi r^{2}+2 \pi r h \) Round your answer to two decimal places. Show all your work.