A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 350 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 0.05 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 = Trh Area of the sides: A = 2rrh Area of the top/bottom: A = Tr To minimize the cost of the package: Radius: cm Height: cm Minimum cost: cents
A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 350 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 0.05 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 = Trh Area of the sides: A = 2rrh Area of the top/bottom: A = Tr 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
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A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 350 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 0.05 cents per square centimeter. Find the dimensions for the package that will minimize production cost.
Transcribed Image Text:A microwaveable cup-of-soup package needs to be
constructed in the shape of cylinder to hold 350 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 0.05 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 = Trh
Area of the sides: A = 2™rh
Area of the top/bottom: A = Tp
To minimize the cost of the package:
Radius:
cm
Height:
cm
Minimum cost:
cents
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