Question

A rectangular box is made from a piece of cardboard that measures 48cm by 18cm by cutting equal squares from each corner and turning up the sides. Find the maximum volume of such a box if:

a) The height of the box must be at most 3cm.

b) The length and width of the base must at least 10cm.

Answer #1

An open box is to be made from a 16-inch by 30-inch piece of
cardboard by cutting out squares of equal size from the four
corners and bending up the sides. What size should the squares be
to obtain a box with the largest volume?
a. Draw and label the diagram that shows length x and width y of
the box.
b. Find the volume formula in terms of x.
c. Find the x value for which the rectangle has...

An open box is to be made from a 2-meters by 6-meters piece of
cardboard by cutting out squares of equal size from the four
corners and bending up the sides. Find the dimensions of the box
that would give the largest volume? Justify your answer by
displaying all work. Make sure to display the proper formulas for
the length and width in terms of x.

A piece of cardboard is twice as long as it is wide. It is to be
made into a box with an open top by cutting 2 cm squares from each
corner and folding up the sides. Let x represent the width of the
original piece of cardboard. Find the width of the original piece
of cardboard,x, if the volume of the box is 1120 cm^3

Metal Fabrication
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 24 in. long and 9 in.
wide, find the dimensions of the box that will yield the maximum
volume.

3. A large box is made from a piece of cardboard that measures
10ft by 10ft . Squares of equal size (side length x) will be cut
out of each corner. The sides will then be folded up to form a
rectangular box.
a) Write down a formula for V(x), the volume of the cardboard
box.
b) What are the critical values for V(x)?
c) What size square should be cut from each corner to obtain
maximum volume?
d) What...

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 14 in. long and 10 in.
wide, find the dimensions of the box that will yield the maximum
volume. (Round your answers to two decimal places.)
_____ in (smallest value)
_____ in
______in(largest value)

An
open box is made out of a 10-inch by 18-inch piece of cardboard by
cutting out squares of equal size from the four corners and bending
up at the sides. find the dimensions of the resulting box that has
the largest volume.
asking for:
Dimensions of the bottom of the box: _ * _
height of box:

An open box is to be made from a 20 cm by 29 cm piece of
cardboard by cutting out squares of equal size from the four
corners and bending up the sides. If ? denotes the length of the
sides of these squares, express the volume ? of the resulting box
as a function of ? .
?(?)= ____ cm/s.

A box (with no top) is to be constructed from a piece of
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You are planning to make an open rectangular box from a 19in by
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