An open-top rectangular box is constructed from a 10-in.-by-16-in. piece of cardboard by cutting squares of equal side length from the corners and folding up the sides. Find analytically the dimensions of the box of largest volume and the maximum volume. Support your answers graphically.

Q: From a thin piece of cardboard 40 in. by 40 in., square corners are cut out so that the sides can be…

A: Given: From a thin piece of cardboard 40 in. by 40 in.

Q: A packaging company is going to make open-topped boxes out of 20 cm by 20 cm rectangles of cardboard…

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Q: A production editor at Weston Publishers decided that the pages of a book should have a 1-in. margin…

A: Consider x as the length and y as the breadth of the rectangle.Then area is A = xy.Since x is length…

Q: A box is to be constructed from a piece of square cardboard whose perimeter is 36 inches by cutting…

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Q: A rectangular square-based open-top container is to be made so as the surface area equals 24 m2.…

A: let the dimensions of container according to question are :lengh=a,width=a, and height =hsurface…

Q: An open box is to be made from a 21 ft by 56 ft rectangular piece of sheet metal by cutting out…

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Q: An open box is to be made from a 15 ft by 40 ft rectangular piece of sheet metal by cutting out…

A:

Q: An open-top bin is to be made from a 15-centimeter by 40-centimeter piece of plastic by removing a…

A: A piece of plastic is 15 cm by 40 cm. Let the square piece be cut of side ‘a’ at each corner of the…

Q: Find the maximum volume of a cylindrical soda can such that the sum of its height and its…

A: we have to find the maximum volume of a cylindrical soda can such that the sum of its height and its…

Q: An оpen box is to be made from a 6 ft by 16 ft rectangular cardboard by cutting out equal squares…

A: We can find the maximum volume of the box as below

Q: An open-top box is to be made from a 36 in. by 27 in. piece of cardboard by removing a square from…

A:

Q: Find the dimensions of a rectangular box of volume 1000cubic inches for which the sum of the…

A: Let x,y,z be the length, breadth and the height of the rectangular boxxyz=1000  and the sum…

Q: Find the dimensions that will minimize the surface area (and hence the cost) of a rectangular fish…

A: Find the dimensions that will minimize the surface area (and hence the cost) of a rectangular fish…

Q: A box is to be constructed from a piece of square cardboard whose perimeter is 36 inches by cutting…

A: A box is to be constructed from a piece of square cardboard whose perimeter is 36 inchesby cutting…

Q: Given a closed box with surface area = 16 and a square bottom, what value of x will maximize the…

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Q: If an open box has a square base and a volume of 104 in.3 and is constructed from a tin sheet, find…

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Q: How tall should the file be to maximize the volume that it can hold?

A:

Q: Find the dimensions of the rectangular box with the largest volume if the total surface area given…

A: It is known that the surfaces area for the rectangular box with edges is x,y and z is 2xy+yz+zx and…

Q: A rectangle is constructed with its base on the​ x-axis and its upper two vertices on the parabola y…

A: Given informationRectangle base is on x axisTop on parabola

Q: An open box is to be made from a 33 ft by 88 ft rectangular piece of sheet metal by cutting out…

A:

Q: An open box is made from a 16 inch by 16 inch piece of cardboard by cutting equal squares from each…

A: This question is based on application of derivative.

Q: The dimensions of a closed rectangular box are measured as 21 cm, 17 cm and 11 cm, respectively with…

A: Given the dimension of the closed rectangular box 21 cm, 17 cm and 11 cm

Q: A box with a square base and open top must have a volume of 512 cubic inches. Find the dimensions of…

A: The solution is given below:

Q: A box with an open top and a square base must have a volume of 32 cubic meters. How do you find the…

A:

Q: A rectangular box has a square base. If the sum of the height and the perimeter of the square base…

A: Explanation of the answer is as follows

Q: A box, open at the top, is to be made from a square piece of cardboard by cutting a square out of…

A:

Q: If you double the length of the radius of a sphere from its original length, what effect does that…

A: Given that: Length of radius of a sphere is doubled.

Q: An open rectangular box has an area of 441 cm2. If its length must be 3 times its width, find its…

A:

Q: If 1200 cm² of material is used to make a closed cardboard box with a square base. Find the exact…

A: This question can be solved using the concept of maxima and minima.

Q: An open box is to be made from a 33 ft by 88 ft rectangular piece of sheet metal by cutting out…

A: You have asked multiple questions, so we will solve the first question for you. The rest can be…

Q: An open-top box is to be made from a 40 in. by 27 in. piece of cardboard by removing a square from…

A:

Q: An open box is to be made from a 21 ft by 56 ft rectangular piece of sheet metal by cutting out…

A:

Q: The base of an aquarium with given volume V is made of slate and the sides are made of glass. If the…

A:

Q: What is the maximum volume of an open box that can be made from a square piece of cardboard, 10in on…

A:

Q: Phil wants to design an open box with a square base with a surface area of 400 square inches. What…

A: We need to find dimensions of a box whose volume is maximum.  & volume = x^2 y

Q: Suppose we have 45 m² of material to build a box with a square bottom and no top. What dimensions…

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Q: A box with no top has a square base. If 64 squared centimeter of material is used, what is the…

A: A box with no top has a square base and 65 cm^2 of material is used

Q: A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular…

A: Given: The total perimeter is 16 feet. The given window is formed by adjoining semicircle to the top…

Q: A box is to be constructed from a piece of square cardboard whose perimeter is 36 inches by cutting…

A: maximum volume

Q: By cutting away identical squares from each corner of a rectangular piece of cardboard and folding…

A: Draw an open made by cutting identical square from each corner of a rectangular piece of cardboard…

Q: Please

A: If we fold it we will get a cuboid with l=10-2x cm, b=8-2x cm and h=x cm Volume V for a cuboid = lbh

Q: A farmer wants to make a rectangluar enclosure using a wall of a barn as one side and 160 ft of…

A: Let x ,in feet, be the length of side of rectangular enclosure which is along the wall of barn and y…

Q: A rectangular plot adjacent to a stream is to be fenced in by using the stream as one side of the…

A: We have to find the maximum area.

Q: An open top box is made by cutting squares from the corners of a piece of tin and folding up the…

A:

Q: An open box is to be made from a square piece of material by cutting equal squares from each corner…

A:

Q: An open box is to be made from a 33 ft by 88 ft rectangular piece of sheet metal by cutting out…

A: Solve the given problem.

Q: A cardboard box without a lid must have a volume of 4m³. - Determine the dimensions that minimize…

A:

Q: The sum of the dimensions of a box with a sqaure base is 48 m. Find the maximum volume of the box.

A: Volume

Q: An open topped box is to be made from a rectangular piece of metal 18cm x 48 cm by cutting off…

A:

Q: Find the dimensions of a open topped box that maximizes the volume with the constraint that the…

A: We will use Lagranges multiplier method to find dimension of the box .