Question

A rectangular box with an open top is to be made from a 13 -in.-by- 48 -in. piece of cardboard by removing small squares of equal size from the corners and folding up the remaining flaps. What should be the size of the squares cut from the corners so that the box will have the largest possible volume?

Answer #1

You are planning to make an open rectangular box from a 9in by
17in piece of cardboard by cutting congruent squares from the
corners and folding up the sides. What are the dimensions of the
box of largest volume you can make this way, and what is its
volume?

You are planning to make an open rectangular box from a 19in by
37 -in. piece of cardboard by cutting congruent squares from the
corners and folding up the sides. What are the dimensions of the
box of largest volume you can make this way, and what is its
volume? The dimensions of the box of the maximum volume are

An
open rectangular box is to be constructed by cutting square corners
out of a20-by-20 inch piece of cardboard and folding up the flaps.
A box formed this way is shown on the right. Find the value of x
for which the volume of the box will be as large as possible.

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).

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)

A 10-inch square piece of metal is to be used to make an
open-top box by cutting equal-sized squares from each corner and
folding up the sides. The length, width, and height of the box are
each to be less than 7 inches. What size squares should be cut out
to produce a box with volume 50 cubic inches?
What size squares should be cut out to produce a box with largest
possible volume?

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.

An
open top box is to be made by cutting small congruent squares from
each corner of a 12x12in sheet of cardboard and folding up sides.
Whag dimensions would yield max volume, using calculus?

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.

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