Minimizing surface area of a shaker

[SpanInq]

Hi, I have an mathematics assignment to do, and I wonder if the topic I have chosen is doable for me. I want to minimize the surface area of a cobbler cocktail shaker, and until now my plan was to get the curve equation for the side of it, and get the area equation from surface of revolution formula and curve equation and then differentiate that. My problem is now finding the curve equation for shaker's side...any ideas how to do that? Tried using GetData software to get datapoints and plotting it, but it doesn't work well.
Thank you for help

 

[SteamKing]

Hi, I have an mathematics assignment to do, and I wonder if the topic I have chosen is doable for me. I want to minimize the surface area of a cobbler cocktail shaker, and until now my plan was to get the curve equation for the side of it, and get the area equation from surface of revolution formula and curve equation and then differentiate that. My problem is now finding the curve equation for shaker's side...any ideas how to do that? Tried using GetData software to get datapoints and plotting it, but it doesn't work well.
Thank you for help

I'm not sure what you hope to obtain by minimizing the surface area of this particular shape.

In any event, if you want to obtain the minimal surface area for a given volume, the sphere is the shape to use, not the shape of this salt shaker.