Question
In: Math
By cutting away an x-by-x square from each corner of a rectangular piece of cardboard and...
By cutting away an x-by-x square from each corner of a rectangular piece of cardboard and folding up the resulting flaps, a box with no top can be constructed. If the cardboard is 6 inches long by 6inches wide, find the value of x that will yield the maximum volume of the resulting box.
Solutions
milcah answered 2 years agoRelated Solutions
By cutting away identical squares from each corner of a rectangular piece of cardboard and folding...
By cutting away identical squares from each corner of a
rectangular piece of cardboard and folding up the resulting flaps,
an open box may be made. If the cardboard is 15 in. long and 7 in.
wide,
(a) Find the dimensions (in inches) of the box that will yield
the maximum volume. (Round your answers to two decimal places if
necessary.)
(b) Which theorem did you use to find the answer?
By cutting away identical squares from each corner of a rectangular piece of cardboard and folding...
By cutting away identical squares from each corner of a
rectangular piece of cardboard and folding up the resulting flaps,
an open box may be made. If the cardboard is 15 in. long and 14 in.
wide, find the dimensions of the box that will yield the maximum
volume. (Round your answers to two decimal places.)
2. Packaging By cutting away identical squares from each corner of a rectangular piece of cardboard...
2.
Packaging
By cutting away identical squares from each corner of a
rectangular piece of cardboard and folding up the resulting flaps,
an open box may be made. If the cardboard is 16 in. long and 6 in.
wide, find the dimensions (in inches) of the box that will yield
the maximum volume. (Round your answers to two decimal places if
necessary.)
smallest value=? in ?in largest value =?in
3.
Minimizing Packaging Costs
A rectangular box is to have a...
a. Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 7 ft by 5 ft.
a. Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 7 ft by 5 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this way.
b. Suppose that in part (a) the original piece of cardboard is a square with sides of length s. Find the volume of the largest box that...
A rectangular piece of cardboard, whose area is 170 square centimeters, is made into an open...
A
rectangular piece of cardboard, whose area is 170 square
centimeters, is made into an open box by cutting a 2- centimeter
square from each corner and turning up the sides. If the box is to
have a volume of 156 cubic centimeters, what size cardboard should
you start with?
A box with an open top is to be constructed from a square piece of cardboard, 5 ft wide, by cutting out a square from each of the four comers and bending up the sides
A box with an open top is to be constructed from a square piece of cardboard, 5 ft wide, by cutting out a square from each of the four comers and bending up the sides. Find the largest volume that such a box can have.
An open rectangular box is made from a 9 inch by 12 inch piece of cardboard...
An open rectangular box is made from a 9 inch by 12 inch piece
of cardboard by cutting squares of side length ? from the corners.
Determine the length of the sides of the square which will maximize
the volume. (Clearly identify the function in terms of one variable
and state the domain, then solve.)
From a thin piece of cardboard 4 in. by 4 in., square corners are cut out...
From a thin piece of cardboard 4 in. by 4 in., square corners
are cut out so that the sides can be folded up to make an open box.
What dimensions will yield a box of maximum volume? What is the
maximum volume?
a. Squares with sides of length x are cut out of each corner of a rectangular...
a. Squares with sides of length x are cut out of each corner
of a rectangular piece of cardboard measuring 5 ft by 4 ft. The
resulting piece of cardboard is then folded into a box without a
lid. Find the volume of the largest box that can be formed in this
way.
b. Suppose that in part (a) the original piece of cardboard
is a square with sides of length s. Find the volume of the largest
box that...
A box with an open top is to being created with a square piece of cardboard...
A box with an open top is to being created with a square piece
of cardboard 8 inches wide, by cutting four identical squares in
each corner. The sides are being folded as well. Find the
dimensions of the box that has the largest volume.
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