A square piece of green origami paper that is 6 inches on a side is being made into a gift box (with no lid) by cutting congruent squares out of each corner, folding up the sides, and taping the edges. What size squares should you cut out for maximum volume? (do the whole problem)

I should cut out squares that are 1 in by 1 in

I should cut out squares that are 1/2 in by 1/2 in

I should cut out squares that are 3 in by 3 in

I should not cut out any squares

A sheet of rectangular cardboard that is 8ft by 12ft is being folded into an open top box. Check all that apply.

The maximum volume of the box is 67.6 cubic feet when the height is 1.57 ft

The dimensions that maximize the volume of the box are 1.57, 4.86, and 8.86

The maximum volume of the box is 68.6 cubic feet when teh height is 1.67 ft

The dimensions that maximize the volume of the box are are 1.67, 4.77, and 8.96

Maximize Volume Quiz

Authored by Anthony Clark

Mathematics

12th Grade

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

A 16cm x 30cm sheet of rectangular cardboard is folded such that an open-top box is created. What is the maximized volume?

$480\ cm^3$

$621\ cm^3$

$730\ cm^3$

$725\ cm^3$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

A 16cm x 30cm sheet of rectangular cardboard is folded such that an open-top box is created. What are the dimensions that maximize the volume?

16cm x 30cm x 0cm

23cm x 9cm x 3 cm

8cm x 15cm x 4cm

23.3cm x 9.3cm x 3.3cm

MULTIPLE SELECT QUESTION

1 min • 1 pt

A 16cm x 30cm sheet of rectangular cardboard is folded such that an open top box is created. What is the volume equation that models all of the boxes that can be from the piece of cardboard? Choose all that apply.

$v\left(x\right)=\left(30-2x\right)\left(16-2x\right)x$

$v\left(x\right)=4x^2-92x+480$

$v\left(x\right)=4x^3-92x^2+480x$

$v\left(x\right)=4x^3+92x^2-480x$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

A closed rectangular shipping box with square base is to be made from 120 square inches of cardboard. What dimensions should the box be for maximum volume? Choose the constraint and optimization equations that represent the problem.

$x^2=120$ and $V=x^3$

$2x+y=120$ and $V=xy$

$x^2y=120$ and $V=2x^2+4xy$

$2x^2+4xy=120$ and $V=x^2y$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

A closed rectangular shipping box with square base is to be made from 120 square inches of cardboard. What dimensions should the box be for maximum volume? Choose the constraint and optimization equations that represent the problem.

$x^2=120$ and $V=x^3$

$2x+y=120$ and $V=xy$

$x^2y=120$ and $V=2x^2+4xy$

$2x^2+4xy=120$ and $V=x^2y$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

A square of side x inches is cut out of each corner of a 10 in x 18 in piece of cardboard and the sides are folded up to form an open-top box. Determine the dimensions of the cut-out squares that will produce the maximum volume.

2.063 in x 2.063 in

2 in x 2 in

168 in x 168 in

2.063 in x 5.873 in x 13. 874 in

FILL IN THE BLANKS QUESTION

1 min • 1 pt

A square of side x inches is cut out of each corner of a 10 in x 18 in piece of cardboard and the sides are folded up to form an open-top box. What is the maximum volume? (Round to the nearest thousandth.)

(a)

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Maximize Volume

A 16cm x 30cm sheet of rectangular cardboard is folded such that an open-top box is created. What is the maximized volume?

A 16cm x 30cm sheet of rectangular cardboard is folded such that an open-top box is created. What are the dimensions that maximize the volume?

A 16cm x 30cm sheet of rectangular cardboard is folded such that an open top box is created. What is the volume equation that models all of the boxes that can be from the piece of cardboard? Choose all that apply.

A closed rectangular shipping box with square base is to be made from 120 square inches of cardboard. What dimensions should the box be for maximum volume? Choose the constraint and optimization equations that represent the problem.

A closed rectangular shipping box with square base is to be made from 120 square inches of cardboard. What dimensions should the box be for maximum volume? Choose the constraint and optimization equations that represent the problem.

A square of side x inches is cut out of each corner of a 10 in x 18 in piece of cardboard and the sides are folded up to form an open-top box. Determine the dimensions of the cut-out squares that will produce the maximum volume.

A square of side x inches is cut out of each corner of a 10 in x 18 in piece of cardboard and the sides are folded up to form an open-top box. What is the maximum volume? (Round to the nearest thousandth.)

(a)

Edgar is making an open-top box from an 12 cm x 16 cm sheet of paper. The volume v(x) is a function of the side length of the square cutout x. Which expression represents v(x)?

Edgar is making an open-top box from an 12 cm x 16 cm sheet of paper. The volume v(x) is a function of the side length of the square cutout x. What interval of values make sense for x the length of the cutout in this situation?

Access all questions and much more by creating a free account

Similar Resources on Wayground

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Discover more resources for Mathematics

Maximize Volume

A 16cm x 30cm sheet of rectangular cardboard is folded such that an open-top box is created. What is the maximized volume?

A 16cm x 30cm sheet of rectangular cardboard is folded such that an open-top box is created. What are the dimensions that maximize the volume?

A 16cm x 30cm sheet of rectangular cardboard is folded such that an open top box is created. What is the volume equation that models all of the boxes that can be from the piece of cardboard? Choose all that apply.

A closed rectangular shipping box with square base is to be made from 120 square inches of cardboard. What dimensions should the box be for maximum volume? Choose the constraint and optimization equations that represent the problem.

A closed rectangular shipping box with square base is to be made from 120 square inches of cardboard. What dimensions should the box be for maximum volume? Choose the constraint and optimization equations that represent the problem.

A square of side x inches is cut out of each corner of a 10 in x 18 in piece of cardboard and the sides are folded up to form an open-top box. Determine the dimensions of the cut-out squares that will produce the maximum volume.

A square of side x inches is cut out of each corner of a 10 in x 18 in piece of cardboard and the sides are folded up to form an open-top box. What is the maximum volume? (Round to the nearest thousandth.) (a)

Edgar is making an open-top box from an 12 cm x 16 cm sheet of paper. The volume v(x) is a function of the side length of the square cutout x. Which expression represents v(x)?

Edgar is making an open-top box from an 12 cm x 16 cm sheet of paper. The volume v(x) is a function of the side length of the square cutout x. What interval of values make sense for x the length of the cutout in this situation?

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

A square of side x inches is cut out of each corner of a 10 in x 18 in piece of cardboard and the sides are folded up to form an open-top box. What is the maximum volume? (Round to the nearest thousandth.)

(a)