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 = π r 2 h V = π r 2 h Area of the sides: A = 2 π r h A = 2 π r h Area of the top/bottom: A = π r 2 A = π r 2

a) To minimize the cost of the package:

b) Radius: cm

c) Height: cm

d) Minimum cost: cents

Answer #1

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 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:

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 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...

Suppose the material for the top and bottom costs b cents per
square centimeter and the material for the sides costs 0.1 cents
per square centimeter. You want to make a can with a volume of k.
What values for the height and radius will minimize the cost? (Your
answer will have a k and a b in it.)

An open-top rectangular box is being constructed to hold a
volume of 300 in3. The base of the box is made from a
material costing 8 cents/in2. The front of the box must
be decorated, and will cost 12 cents/in2. The remainder
of the sides will cost 2 cents/in2.
Find the dimensions that will minimize the cost of constructing
this box.
Front width: _______ in.
Depth: ________ in.
Height: ________ in.

A pencil cup with a capacity of 48 in^3 is to be constructed in
the shape of a rectangular box with a square base and an open top.
If the material for the sides costs 40¢/in^2 and the material for
the base costs 60¢/in.^2, what should the dimensions of the cup be
to minimize the construction cost? A pencil cup is in the shape of
a rectangular box with a square base and an open top.
height ____ in
length...

A circular cylinder with a radius R of 1 cm and a height H of 2
cm carries a charge density of pv = h R^2 uC/cm^3 (h is a point on
the z-axis). The cylinder is then placed on the xy plane with its
axis the same as the z-axis. Find the electric field intensity E
and and the electric potential V on point A on z-axis 2 cm from the
top of the cylinder.

An energy drink container in the shape of a right circular
cylinder must have a volume of 19 fluid ounces (1 fluid ounce is
approximately 1.80469 cubic inches). The cost per square inch of
constructing the top and bottom is twice the cost of constructing
the lateral side. Find the dimensions that will minimize the cost.
(Round your answers to two decimal places.)
r
=
h
=

10. A circular cylinder with a radius R of 1 cm and a
height H of 2 cm carries a charge density of ρV = H r2 sin φ µC/cm3
(r is a point on the z-axis, φ is an azimuthal angle). The cylinder
is then placed on the xy plane with its axis the same as the
z-axis. Find the electric field intensity E and the electric
potential V on point A on z-axis 2 cm from the top...

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