Question

A box with an open top is to be constructed from a square piece of cardboard, 6 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have (round your answer to the nearest thousandth).

Answer #1

A box with an open top is to be constructed from a square piece
of cardboard, 22 in. wide, by cutting out a square from each of the
four corners and bending up the sides. What is the maximum volume
of such a box? (Round your answer to two decimal places.)

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.

A box (with no top) is to be constructed from a piece of
cardboard of sides A and B by cutting out squares of length h from
the corners and folding up the sides. Find the value of h that
maximizes the volume of the box if A=6 and B=7.

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 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 box with an open top is made from a square sheet of cardboard
with an area of 10,000 square in. by cutting out squares from the
corners and folding up the edges. Find the maximum volume of a box
made this way. (draw a picture).

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 formed from a piece of 8 by 10 inch cardboard by
cutting out corners and folding up the sides. Find the maximum
volume of the box formed this way and give the dimensions.

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.

Rectangular box is made from a piece of cardboard that is 24
inches long
and 9 inches wide by cutting out identical squares from the four
corners and turning up
the sides. Find the dimensions of the box of maximum volume. What
is this maximum
volume?

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