The diagram shows a square prism with cross-section x units by x units, and length (9- 2x) units. What is the maximum volume of the prism?

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Q: An open rectangular box is 22feet long and has a surface area of 96 square feet. Find the dimensions…

A: Given, length of box is 22 feet and surface area are 96 square feet.

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

Q: Kelly has 2,400 ft. of irrigation piping he wants to use to irrigate his back lawn. He wants to lay…

A: Given query is to find the the dimension of the rectangle.

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Q: Mr. Camu wants to enclose his vegetable garden at the back of his estate with a fence on 3 sides. He…

A: Since Mr. Camu has 30m of fencing. As he wants to enclose his vegetable garden with a fence on 3…

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A: It's given that the box has a square base. However, nothing is said about the the height.  Let the…

Q: A Norman window has the shape of a rectangle surmounted by a semicircle of diameter equal to the…

A: Draw the rough diagram as shown below. From the above figure, it is observed that, Perimeter…

Q: An open box is to be made of a piece of cardboard 10cm x 16cm by cutting equal squares out of the…

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Q: A cardboard box without a lid is to have volume 100 cubic inches with the total area of cardboard as…

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Q: Three hundred square inches of material are available to construct an open rectangular box with a…

A: Given: Three hundred square inches of material are available to construct an open rectangular box…

Q: DAUST's students plan to design a closed box with a square base and a surface area of 90 cm2 for…

A: If the side of square base is 'a'cm and length is 'b'cm Than surface area will be a2b

Q: Example Find the dimensions of the rectangular box with an open top with largest volume if the total…

A: Given : Total surface area of the rectangular box is 216 cm²

Q: An open cardboard box is to be made with a volume of 4m'. Find the dimension of the box that…

A: Volume has given, we use surface area of cardboard to solve following question

Q: Having 3m2 of aluminum foil at your disposal, you want to build a rectangular box with a lid, in…

A: The volume of the rectangular box is V= xyz, where x, y, & z are the length, breadth, &…

Q: 4. A rectangular box is to be made from a piece of cardboard 15cm by 24 cm by cutting equal squares…

A: A rectangular box is to be made from a piece of cardboard 15 cm by 24 cm by cutting equal squares…

Q: 2) The diagram shows a square with cross-section x units by x units, and 9- 2x units. Find maximum…

A: From the given diagram; The expression for the volume of the given prism is:…

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

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Q: How many square units is the area of the region bounded by the parabolas y = x^2 and y = -x^2 + 4x ?

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Q: (U.1. 6. Find the dimensions of the closed rectangular box of largest volume with surface area of 16…

A: Surface area of the closed rectangular box:(with square bases) and height h;2x2+4xh…

Q: What is the maximum size of the window frame you can create with 20 feet of materials? The window…

A: To Find: The maximum size of the window frame you can create with 20 feet of materials.

Q: A rancher has 960 feet of fencing to construct six​ corrals, as shown in the figure. Find the…

A: Given: Length of rancher = x Width = y Fencing = 960 feet:   To find: Maximum possible are with…

Q: A cardboard piece that is 12 inches by 10 inches. It is required to cut out the corners as shown…

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Q: A rectangular box is to have a base whose width is twice the length and is to have no top. If the…

A: Given, A rectangular box is to have a base whose width is twice the length and is to have no top.…

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A: Let the length of small square = x Hence, length of the big square = 15 - x - x = 15 - 2x Therefore,…

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Q: Q2. Calculate the maximum volume that can be got from a rectangular sheet (4cmx3cm). The sheet is…

A: To solve this problem, we have to obtain the volume of the open box as a function of some variable x…

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Q: The perimeter of an isosceles triangle is 42 cm.  Find the maximum area of the isosceles triangle…

A: Let's find.

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Q: A rain gutter is made from sheets of aluminum that are 20 inches wide by turning up the edges to…

A: Suppose A be the area of the rectangular rain gutter  A=length × width=20-2x x…

Q: A window is in the shape of a rectangle surrounded by a semicircle. If the perimeter of the window…

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Q: A farmer has 416 feet of fence in which to fence in the rectangular area with 2 dividers as shown to…

A: Given: Totol length of fence = 416ftLet say for rectangular regionLength = L (ft)Width = W (ft)Now…

Q: Alex wants to design a beach cabana tent with a rectangular box shape. The tent will have two square…

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Q: 8. A rancher has 200 feet of fencing with which to enclose two adjacent rectangular corrals (see…

A: A rectangular figure is given. Let, the length of parallel side of division be y and the length of…

Q: You have 300 feet of fencing to construct a rectangular pen for cattle. What are the dimensions of…

A: Let x be the length and y be the width of the pen. According to given, 2(x+y)= 300 150=x+y y=…

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A: The solution are next step

Q: A 10 m? plastic is to be used to form a hollow cylinder that has a circular base and| an open top.…

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Q: closed box with a square base is to contain 252 cubic feet. The bottom costs $5 per square ot, the…

A: Please refer to the image below

Q: Define the livable space of a building to be the volume of space in the building where a person 6…

A: As given that height of the rectangular box= 6 ft. (according to the height of person) Length of the…

Q: A cardboard box in the shape of a rectangular prism without a lid is to have a volume of 62,500 cm3.…

A: Use formula, V=x^2+h A=x^2+4xh.

Q: A rectangular box without a lid is to be made from 12 m2 of cardboard. Find the maximum volume of…

A: Given that a rectangular box without a lid is to be made from 12 m² of cardboard.

Q: A close rectangular box where length is double its width has a total surface of 300 square inches.…

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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.

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Q: A carpenter is building a rectangular room with a fixed perimeter of 116 ft. What dimensions would…

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Q: An open rectangular box is 4 feet long and has a surface area of 48 square feet. Find the dimensions…

A: Let w and h (in feet) be the width and height of the open box. Length of the box is l=4 feet Surface…