A cylinder shaped can needs to be constructed to hold 350 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 0.07 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=πr2hV=πr2h Area of the sides: A=2πrhA=2πrh Area of the top/bottom: A=πr2A=πr2 To minimize the cost of the can: Radius of the can: Height of the can:
A cylinder shaped can needs to be constructed to hold 350 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 0.07 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=πr2hV=πr2h Area of the sides: A=2πrhA=2πrh Area of the top/bottom: A=πr2A=πr2 To minimize the cost of the can: Radius of the can: Height of the can:
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...
Related questions
Question
100%
A cylinder shaped can needs to be constructed to hold 350 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 0.07 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=πr2hV=πr2h
Area of the sides: A=2πrhA=2πrh
Area of the top/bottom: A=πr2A=πr2
To minimize the cost of the can:
Radius of the can:
Height of the can:
Minimum cost:
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell