A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 550 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.03 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 = 2πrh Area of the top/bottom: A = Tr² To minimize the cost of the package: Radius: Height: Minimum cost: cm cm cents
A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 550 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.03 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 = 2πrh Area of the top/bottom: A = Tr² To minimize the cost of the package: Radius: Height: Minimum cost: cm cm 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
Section9.2: Pyramids, Area, And Volume
Problem 33E
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Question
![A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 550 cubic
centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.03 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 = 2πrh
Area of the top/bottom: A = Tr²
To minimize the cost of the package:
Radius:
Height:
Minimum cost:
cm
cm
cents](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F621ac9f8-2dbb-4715-ab7b-42c3ebc90b44%2Fe38524f8-64cf-45ff-8fd3-cdf169fd6296%2F2ts11s8_processed.png&w=3840&q=75)
Transcribed Image Text:A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 550 cubic
centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.03 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 = 2πrh
Area of the top/bottom: A = Tr²
To minimize the cost of the package:
Radius:
Height:
Minimum cost:
cm
cm
cents
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