Question

A box with an open top has a square base and four sides of equal height. The volume of the box is 225 ft cubed. The height is 4 ft greater than both the length and the width. If the surface area is 205 ft squared. what are the dimensions of the box?

What is the width of the box?.

What is the length of the box?

Answer #1

An open rectangular box (no top) is formed with a square base
and rectangular sides so that the total volume enclosed is 475 cu.
ft. What is the smallest amount of material (area) that can form
such a box?

A box with a square base and open top must have a volume of
202612 cm3. We wish to find the dimensions of the box that minimize
the amount of material used.
(Round your answer to the nearest tenthousandths if
necessary.)
Length =
Width =
Height =

A box with a square base and open top must have a volume of
296352 cm3. We wish to find the dimensions of the box that minimize
the amount of material used.
(Round your answer to the nearest tenthousandths if
necessary.)
Length =
Width =
Height =

A box with a square base and open top must have a volume of
108000 cm^3. We wish to find the dimensions of the box that
minimize the amount of material used.
First, find a formula for the surface area of the box in terms of
only x, the length of one side of the square base.
[Hint: use the volume formula to express the height of the box in
terms of x.]
Simplify your formula as much as possible....

A box with a square base and open top must have a volume of
157216 cm3cm3. We wish to find the dimensions of the box that
minimize the amount of material used.
First, find a formula for the surface area of the box in terms of
only xx, the length of one side of the square base.
[Hint: use the volume formula to express the height of the box in
terms of xx.]
Simplify your formula as much as possible....

A rectangular box is to have a square base and a volume of 16
ft3. If the material for the base costs
$0.14/ft2, the material for the sides costs
$0.06/ft2, and the material for the top costs
$0.10/ft2, determine the dimensions (in ft) of the box
that can be constructed at minimum cost. (Refer to the figure
below.)
A closed rectangular box has a length of x, a width of
x, and a height of y.

Problem: A box with an open top is to be constructed from a
square piece of cardboard, with sides 6 meters in length, by
cutting a square from each of the four corners and bending up the
sides. Find the dimensions that maximize the volume of the box and
the maximum volume.

Minimizing Packaging Costs A rectangular box is to have a square
base and a volume of 20 ft3. If the material for the base costs
$0.28/ft2, the material for the sides costs $0.10/ft2, and the
material for the top costs $0.22/ft2, determine the dimensions (in
ft) of the box that can be constructed at minimum cost. (Refer to
the figure below.) A closed rectangular box has a length of x, a
width of x, and a height of y. x...

A rectangular storage container with an open top has a volume of
10 m3 . The length of the base is twice its width. Material for the
base costs $10 per sqaure meter and material for the sides costs $6
per square meter. (a) Find an equation for the volume of the box,
relating the variables of the height of the box and the width of
the base of the box. (b) Use the previous equation to solve for the...

A company plans to manufacture a rectangular box with a square
base, an open top, and a volume of 404 cm3. The cost of the
material for the base is 0.5 cents per square centimeter, and the
cost of the material for the sides is 0.1 cents per square
centimeter. Determine the dimensions of the box that will minimize
the cost of manufacturing it. What is the minimum cost?

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