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 0.03 cents per square centimeter. The top will be made of glued paper, costing 0.08 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 = ²h Area of the sides: A = 2πrh Area of the top/bottom: A = To minimize the cost of the package (round to 2 decimal places): Radius: Height: Minimum cost: πr² cm cm cents Question Help: Video Message instructor Submit Question Jump to Answer
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 0.03 cents per square centimeter. The top will be made of glued paper, costing 0.08 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 = ²h Area of the sides: A = 2πrh Area of the top/bottom: A = To minimize the cost of the package (round to 2 decimal places): Radius: Height: Minimum cost: πr² cm cm cents Question Help: Video Message instructor Submit Question Jump to Answer
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 29E
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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 0.03 cents
per square centimeter. The top will be made of glued paper, costing 0.08 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 = ²h
Area of the sides: A = 2πrh
Area of the top/bottom: A
=
To minimize the cost of the package (round to 2 decimal places):
Radius:
Height:
Minimum cost:
πr²
cm
cm
cents
Question Help: Video Message instructor
Submit Question Jump to Answer
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