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A cylinder shaped can needs to be constructed to hold 250 cubic centimeters of soup. The material for the sides of the can costs 0.02 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.08 cents per square centimeter. Find the dimensions for the can that will minimize production cost. Helpful information: h : height of can, r : radius of can Volume of a cylinder: V = Area of the sides: A 2Trh %3D Area of the top/bottom: A = Tr² To minimize the cost of the can: Radius of the can: Height of the can: Minimum cost: cents

A cylinder shaped can needs to be constructed to hold 250 cubic centimeters of soup. The material for the sides of the can costs 0.02 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.08 cents per square centimeter. Find the dimensions for the can that will minimize production cost. Helpful information: h : height of can, r : radius of can Volume of a cylinder: V = Area of the sides: A 2Trh %3D Area of the top/bottom: A = Tr² To minimize the cost of the can: Radius of the can: Height of the can: Minimum cost: cents

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 cylinder shaped can needs to be constructed to hold 250 cubic centimeters of soup. The material for the sides of the can costs 0.02 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.08 cents per square centimeter. Find the dimensions for the can that will minimize production cost. Helpful information: h: height of can, r: radius of can Volume of a cylinder: V = T Area of the sides: A = 2arh Area of the top/bottom: A To minimize the cost of the can: Radius of the can: Height of the can: Minimum cost: cents
Transcribed Image Text:A cylinder shaped can needs to be constructed to hold 250 cubic centimeters of soup. The material for the sides of the can costs 0.02 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.08 cents per square centimeter. Find the dimensions for the can that will minimize production cost. Helpful information: h: height of can, r: radius of can Volume of a cylinder: V = T Area of the sides: A = 2arh Area of the top/bottom: A To minimize the cost of the can: Radius of the can: Height of the can: Minimum cost: cents
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