Originally Posted by

**Goose** A fuel tank is being designed to contain 200 m^3 of gasoline; however, the maximum length tank that can be safely transported to clients is 16 m long. The design of the tank calls for a cylindrical part in the middle with hemispheres at the end. If the hemispheres cost $2/unit and the cylindrical wall costs $1/unit, find the radius and height of the cylinder part so that the cost of manufacturing the tank will be minimal. Give the answer correct to the nearest centimeter.

Here's what I have so far:

V= πr^2h + 4/3πr^3

200= πr^2h + 4/3πr^3

(200 - 4/3πr^3)/(πr^2)= h

SA= 4πr^2 + 2πrh

= 4πr^2 + 2πr[(200 - 4/3πr^3)/(πr^2)]

**= 4πr^2 + (400πr - 8/3π^2r^4)/r^2**

C= 8πr^2 + (400πr - 8/3π^2r^4)/(πr^2)

C'= 16πr - [16(r^3π + 75)]/3r^2 ??

I'm pretty lost and I'm sure I made several large errors because this is just not making sense. Any help is very much appreciated. Thanks!