A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 250 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.02 cents fer square centimeter. The top will be made of glued paper, costing 0.06 cents 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 = Tr2h Area of the sides: A = 27Trh Area of the top/bottom: A = Tr² To minimize the cost of the package: Radius: cm Height: cm Minimum cost: cents

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
icon
Related questions
Question
A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 250 cubic
centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.02 cents fer
square centimeter. The top will be made of glued paper, costing 0.06 cents 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 = Tr2h
Area of the sides: A = 2Trh
Area of the top/bottom: A = Tr²
To minimize the cost of the package:
Radius:
cm
Height:
cm
Minimum cost:
cents
Transcribed Image Text:A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 250 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.02 cents fer square centimeter. The top will be made of glued paper, costing 0.06 cents 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 = Tr2h Area of the sides: A = 2Trh Area of the top/bottom: A = Tr² To minimize the cost of the package: Radius: cm Height: cm Minimum cost: cents
Expert Solution
steps

Step by step

Solved in 3 steps

Blurred answer
Similar questions
Recommended textbooks for you
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning