Question

In: Math

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?

Expert Solution

So these are critical points!

So dimensions are

So maximum volume is 128/27 in³

milcah answered 2 years ago

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.

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.

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.

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 10 inch by 16 inch piece of cardboard by cutting squares of equal sides length from the corners and folding up the sides

A box with an open top is to be constructed from a 10 inch by 16 inch piece of cardboard by cutting squares of equal sides length from the corners and folding up the sides. Find the dimensions of the box of largest volume that can be constructed.

Place 4 charges at the corners of a square which is 2 meters by 2 meters...

Place 4 charges at the corners of a square which is 2 meters by 2 meters (4 large squares along each length). Place two +1 nC charges at adjacent corners and two -1 nC charges at the other two corners. Determine the direction of the electric field at the following three points: Point E halfway between two like charges. (-120 degrees, 50 V/m) Point F halfway between two opposite charges. (-90.5 degrees, 309 V/m) Point G at the center of...

4 charges are fixed to the corners of a square of side .53 cm. Charge 1...

4 charges are fixed to the corners of a square of side .53 cm. Charge 1 of -1 uC is fixed to the top left corner. Charge 2 of -2uC is fixed to the top right corner, charge 3 of 3uC is fixed to the bottom left corner , and charge 4 of -4uC is fixed to the bottom right corner. a) find the magnitude and direction of the electric field at the center of the square b) find the...

An open-top box is to be made from a 20cm by 30cm piece of cardboard by...

An open-top box is to be made from a 20cm by 30cm piece of cardboard by removing a square from each corner of the box and folding up the flaps on each side. What size square should be cut out of each corner to get a box with the maximum volume?

A box with an open top is to be constructed out of a rectangular piece of cardboard with dimensions length=9 ft

A box with an open top is to be constructed out of a rectangular piece of cardboard with dimensions length=9 ft and width=6 ft by cutting a square piece out of each corner and turning the sides up as shown in the picture. Determine the length x of each side of the square that should be cut which would maximize the volume of the box.