# Minimizing Surface Area/Volume

1. Nov 17, 2009

### Mldancer125

1. The problem statement, all variables and given/known data
I need to find a solution to make a large capsule ( top and bottom are hemispheres and middle is a cyliner) The capsule must be big enough to hold .25 cubic meters of medicine. One hemisphere's materials costs $.0025 per square centimeter and the other hemisphere and cylinder materials costs$ .0015 per square centimeter. I need to know the optimal measurements to minimize the total materials cost for the case, as well as the total materials cost for this optimal design.

2. Relevant equations

V of sphere= 4/3pi r^3
V of cylinder= pi r^2h
SA of sphere=4 pi r^2
SA of cylinder= 2pi r^2+ 2pi rh

3. The attempt at a solution

2. Nov 17, 2009

### tiny-tim

Welcome to PF!

Hi Mldancer125! Welcome to PF!

Show us what you've tried, and where you're stuck, and then we'll know how to help!