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A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 400 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.03 dollars per square centimeter. The top will be made of glued paper, costing 0.05 dollars per square centimeter. Find the dimensions for the package that will minimize production cost. Helpful information: h: height of cylinder, r: radius of cylinder Volume of a cylinder: V = Tr’h Area of the sides: A = 2rrh Area of the top/bottom: A = Tr² To minimize the cost of the package: Radius: cm Height: cm Minimum cost: dollars

A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 400 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.03 dollars per square centimeter. The top will be made of glued paper, costing 0.05 dollars per square centimeter. Find the dimensions for the package that will minimize production cost. Helpful information: h: height of cylinder, r: radius of cylinder Volume of a cylinder: V = Tr’h Area of the sides: A = 2rrh Area of the top/bottom: A = Tr² To minimize the cost of the package: Radius: cm Height: cm Minimum cost: dollars

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter59: Areas Of Rectangles, Parallelograms, And Trapezoids
Section: Chapter Questions
Problem 79A
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A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 400 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.03 dollars per square centimeter. The top will be made of glued paper, costing 0.05 dollars per square centimeter. Find the dimensions for the package that will minimize production cost. Helpful information: h: height of cylinder, r: radius of cylinder Volume of a cylinder: V = Tr’h Area of the sides: A = 2rrh Area of the top/bottom: A = Tr² To minimize the cost of the package: Radius: cm Height: cm Minimum cost: dollars
Transcribed Image Text:A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 400 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.03 dollars per square centimeter. The top will be made of glued paper, costing 0.05 dollars per square centimeter. Find the dimensions for the package that will minimize production cost. Helpful information: h: height of cylinder, r: radius of cylinder Volume of a cylinder: V = Tr’h Area of the sides: A = 2rrh Area of the top/bottom: A = Tr² To minimize the cost of the package: Radius: cm Height: cm Minimum cost: dollars
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