A cardboard box without a lid is to have a volume of 32,000 cm^3. Find the dimensions that minimize the amount of cardboard used.

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Q: A box with a square base and an open top must have a volume of 96 cubic inches. If the bottom is…

A: Given that the box has a square base and is open at the top. Since the base of the box is a square,…

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A: To find the dimension of the storage box that will minimize the cost.

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Q: The rectangular bird sanctuary with one side along a straight river is to be constructed so that it…

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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…

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Q: A square piece of cardboard of side a is used to make an open-top box by cutting out a small square…

A: Since, a square piece of cardboard of side 'a' is used to make an open-top box by cutting out a…

Q: A closed rectangular box is to have a volume of 250 cubic centimeters. If the material for the top…

A: Given:  Volume=250 cm3

Q: Find the dimensions of a cylinder of volume 5 m3 of minimal cost if the top and bottom are made of…

A: In order to solve this problem, first we need to find the expression that represents the total cost.…

Q: A fence is to be built around a rectangular area of 36 square metres beside a building where one of…

A: Let x be the length and y be the width of the rectangle One side of the rectangle have no fence. So…

Q: is this question talking about a rectangle within a rectangle?

A: Find the dimensions for the whole poster.

Q: A rectangular portion of a pasture next to an irrigation canal is to be enclosed by a fence with no…

A: We have given a rectangular portion of a pasture. The area of the rectangular pasture = 87362 square…

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

A: Assume that side of square which should be cut from each corner is a.Given the dimension of piece of…

Q: Find the maximum and minimum volumes of a rectangular box whose, surface area is 1300 cm² and whose…

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Q: The Soup Company is constructing an open-top, square-based, rectangular metal tank that will have a…

A: Let dimension of tank be a*a*hBase area=a*a=a2height of tank=hgiven,   volume=32+t3   a2h=32…

Q: A box with a square base and open top must have a volume of4000 cm^3. Find the dimensions of the box…

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Q: A rectangular plot of playground with a 500 m^2 area is to be surrounded by a fence, with an…

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Q: Find the dimensions of a closed rectangular box with a square base and volume 3375 in3 that can be…

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Q: a rectangular property has three sides fenced in against an existing river by 1,200 feet of wooden…

A: Consider the given information.

Q: An open box will be made by cutting a square from each corner of a 10-cm by 16-cm piece of cardboard…

A: To find: The size of square to be cut from the corner of cardboard to maximize volume and also find…

Q: An open box is constructed by cutting square corners with side x cm from a 150-cm by 100-cm sheet of…

A: According to the problem, we have

Q: The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm. The area…

A: 5. Notice that the dimensions of the poster are: Length = x +16, Width = y +24 Area of the Printed…

Q: A rectangular lot having an area of 5000 sq meters is to be fenced on three sides Find the minimum…

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Q: Find the dimensions of the closed rectangular box of largest volume with surface area of 16 m². What…

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Q: Hi, I am wondering how to do the work for this problem and what the final answer would be. Thank you

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Q: poster is to contain 150 square inches of printed matter, surrounded by margins that are 3 inches…

A: Topic = Application of Derivative

Q: A poster needs to have 75 square inches of printed material with margins of 5 inches at the top and…

A: Given: Area of rectangular page = 75 square inches Also, we have margins of 5 inches at the top and…

Q: A manufacturer wants to design an open box having a square base and a surface area of 244 square…

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Q: A Box with a Square base and an open Top must have a volume of 500 cm'. Find the dimensions of the…

A: A box with a square base and an open top must have a volume of 500 cm. To find: The dimensions of…

Q: A farmer wants to construct a fence around an area of 6936 square feet in a rectangular field and…

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Q: A box with a square base with side length b and height h and with an open top must have a volume of…

A: Question is solved.

Q: from a piece of cardboard that is 24 cm by 48 cm ,cut equal squares out of the corners . fold up the…

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Q: A builder intends to construct a storage shed having a volume of 900 cubic feet, and flat roof, and…

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Q: A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing…

A: Given query is to find the dimensions of the gardern to minimize the cost.

Q: Suppose a farmer wants to fence off a rectangular field alongside a river with a total area of 15,…

A: Given, Area= 15000m2 we draw a diagram according to the question we have to find the dimension of…

Q: A rancher plans to make four identical and adjacent rectanglar pens against the barn each with an…

A: Let the length and width of the rectangular pen against barn be x and y. Consider the four identical…

Q: The base of an aquarium (in the shape of a cuboid) with given volume V is made of slate and the…

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Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

A: Find the dimensions of the rectangular box of maximum volume formed by a given rectangular sheet.

Q: Find the maximum volume of a rectangular box with no top that has a surface area of 48 square…

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Q: A box with a square base and open top must have a volume of 32000 cm³. Find the dimensions of the…

A: To find the dimensions of the box that minimize the amount of material used to construct it.

Q: A square-based, box-shaped shipping crate is designed to have a volume of 36 cubic feet. The…

A: Volume=x2y=36 ............equation(1) Cost=2x22k+4xyk Cost=4kx2+xy........equation(2) Form equation…

Q: Find the minimum cost of a rectangular box of volume 200 cm³ whose to

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Q: landscape architect wished to enclose a rectangular garden on one side by a brick wall costing…

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Q: You have been asked to design a 1L oil can shaped like a right circular cylinder with open top. What…

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Q: A box with a volume of 8 m3 is to be constructed with a gold-platedtop, silver-plated bottom, and…

A: Given: Volume of the cube is V=8m3. Cost of gold plating Cg=$120 per square meter. Cost of Silver…

Q: A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing…

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