Question

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 0.03 cents per 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.

To minimize the cost of the package:

Radius:

Height:

Minimum cost:

Answer #1

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
0.04 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:
radius, height, and minimum cost

A microwaveable cup-of-soup package needs to be constructed in
the shape of a cylinder to hold 550 cubic centimeters of soup. The
sides and bottom of the container will be made of syrofoam costing
0.03 cents per 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.

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 0.07 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=πr2hV=πr2h...

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...

A cylinder shaped can needs to be constructed to hold 400 cubic
centimeters of soup. The material for the sides of the can costs
0.04 cents per square centimeter. The material for the top and
bottom of the can need to be thicker, and costs 0.05 cents per
square centimeter. Find the dimensions for the can that will
minimize production cost.
Helpful information:
h : height of can, r : radius of can
Volume of a cylinder: V=πr2^h
Area of...

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height ____ in
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A pencil cup with a capacity of 16 in.3 is to be
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Minimizing Costs A pencil cup with a capacity of 45 in.^3 is to
be constructed in the shape of a rectangular box with a square base
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the material for the base costs 90¢/in.^2, what should the
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A company is designing an aquarium in the shape of a vertical
cylinder for a client. It will have a round base made of slate, the
curved sides are made of plexiglass, and the round top is glass.
The tank must hold 24 cubic feet (about 180 gallons) of water.
Plexiglass costs $8 per square foot, slate costs $6 per square
foot, and glass costs $4 per square foot. Find the dimensions
(rounded to 2 decimal places) the company should...

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