A cylinder shaped can needs to be constructed to hold 200 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 0.06 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 πr² h = Area of the sides: A = 2πrh Area of the top/bottom: A πr ² = 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 200 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 0.06 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 πr² h = Area of the sides: A = 2πrh Area of the top/bottom: A πr ² = To minimize the cost of the can: Radius of the can: Height of the can: Minimum cost: cents

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.1: Prisms, Area And Volume

Problem 27E: The box with dimensions indicated is to be constructed of materials that cost 1 cent per square inch...

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