Minimizing surface area of a shaker

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SUMMARY

The discussion focuses on minimizing the surface area of a cobbler cocktail shaker as part of a mathematics assignment. The user intends to derive the curve equation for the shaker's side and apply the surface of revolution formula to calculate the area. However, they encounter difficulties in obtaining accurate data points using GetData software for plotting. A suggestion is made that, for minimizing surface area for a given volume, a sphere is the optimal shape, rather than the shaker's design.

PREREQUISITES
  • Understanding of calculus, specifically differentiation techniques.
  • Familiarity with surface area calculations using the surface of revolution formula.
  • Basic knowledge of curve equations and their applications in geometry.
  • Experience with data plotting software, such as GetData.
NEXT STEPS
  • Research the surface of revolution formula in detail.
  • Learn how to derive curve equations for various geometric shapes.
  • Explore optimization techniques in calculus, particularly for minimizing surface area.
  • Investigate alternative data plotting tools that may yield better results than GetData.
USEFUL FOR

Students in mathematics, particularly those focusing on calculus and geometry, as well as anyone interested in optimization problems related to surface area and volume.

SpanInq
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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
sha_usagi500xh_0000_stl_web1_1.jpg
 
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SpanInq said:
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
sha_usagi500xh_0000_stl_web1_1.jpg
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.
 

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