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# Optimization - Find the surface area of a domed cylinder?

## Question

###### Optimization - Find the surface area of a domed cylinder?

"A metal storage tank with fixed volume V = 360pi m^3 is to be constructed from a right cylinder (including bottom) surmounted by a hemisphere. What dimensions will require the least amount of material?"

For surface area I used: 2(pi)rh + 3(pi)r^2 simplified to (pi)r(2h+3r)
To remove one of the variables I used: (pi)r(2(360/r^2)+3r)
The derivative is (6pi(r^3-120))/r^2

I'm not sure what to do after this however.

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