A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 200 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.02 cents per square centimeter. The top will be made of glued paper, costing 0.07 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 2rrh Area of the top/bottom: A %3D 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
100%

Plz help me 

A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 200 cubic
centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.02 cents per
square centimeter. The top will be made of glued paper, costing 0.07 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
2
Volume of a cylinder: V = Tr
Area of the sides: A
2rrh
,2
Area of the top/bottom: A
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 200 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.02 cents per square centimeter. The top will be made of glued paper, costing 0.07 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 2 Volume of a cylinder: V = Tr Area of the sides: A 2rrh ,2 Area of the top/bottom: A To minimize the cost of the package: Radius: cm Height: cm Minimum cost: cents
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

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,
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning