2. Design the optimal cylindrical container that is open at one end and has wallsof negligible thickness. The container is to hold 0.2 m³. Design it so that the areasof its bottom and sides are minimized. Use the most efficient numerical methodof solving the optimum values.Openr11T1Th

Consider the given diagram, The the area of the cylinder will be, A=πr2+2πrh The volume of the…

Answered: 2. Design the optimal cylindrical…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Assume that a cylinder has a fixed volume of 125 m³ with an open top. Find the radius and height of the cylinder that can minimize its surface area. The surface area of the cylinder is A = (radius)2 + 2 radius height The volume of the cylinder = (radius)². height. → radius height
If V=R\power{3}, and W\index{1} is the xy plane and let W\index{2} is yz-plane: W\index{1}={(x,y,0):x,y∈R} W\index{2}={(0,y,z):y,z∈R} then V is not the direct sum of W\index{1} and W\index{2}.
Rain is designing a new bottle for Luscious Curls shampoo. The bottle should have a volume of 450 cm³. The company they work for wants to minimize the amount of plastic used per bottle, however the company would like to have a choice between two B3 of three shapes; a cylinder, triangular prism, or rectangular prism. Help Rain to determine the most efficient dimensions of the two most efficient shapes for the bottle with the minimum surface area.Also calculate the surface area of the shapes. Show your work. Bottle choice 1 Bottle choice 2 Bottle choice 1 Bottle choice 2 show your work here Shape and dimensions Shape and surface area
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2. Design the optimal cylindrical container that is open at one end and has walls of negligible thickness. The container is to hold 0.2 m³. Design it so that the areas of its bottom and sides are minimized. Use the most efficient numerical method of solving the optimum values. Open h