Minimum-surface-area box Of all boxes with a square baseand a volume of 8 m3, which one has the minimum surface area?(Give its dimensions.)

Q: 2. An open box is to be made from a square piece of material by cutting equal squares from each…

A: An open box is to be made from a square piece of material by cutting equal squares from eachcorner…

Q: A rectangular tank with a square base, an open top, and a volume of 32ft^3 is to be constructed of…

A: Let side of square base be x ft and height be y ft Given, Volume=32 ft3 X2y = 32, y = 32/x2 – i)…

Q: Example: Suppose a box with no top is to hold a certain volume V. Find the dimensions for the box…

A: The maximum or minimum value of the function given the constraint can be calculated by using the…

Q: 1. A rectangular box has a square base. The combined length of a side of the square base, and the…

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Q: A rectangular solid with a square base has a volume of 5,832 cubic inches. (Let w represent the…

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Q: Eind the dimensions of arect-ongular box the top having of open at -Volume 3 32 m

A: To Determine: The dimensions of a rectangular  box whose volume is 32 m3.

Q: You have been asked to design a rectangular box with a square base and an open top. The volume of…

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Q: 2) The volume of an open box with a square base is 4,000 cubic centimeter (cc). Find the dimensions…

A: The volume of an open box with a square base is 4,000 cubic cm.

Q: A closed rectangular box with faces parallel to the coordinate planes has one bottom corner at the…

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Q: Arectangular tank with a square base, an open top, and a volume of 13,500 ft° is to be constructed…

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Q: The minimum surface area for a given volume of a Occurs when the height is equal to the O length,…

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Q: EXERCISES A. A box with a square base and open top must have a volume of 256 cm Fimd the dimensions…

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Q: 20. Minimizing surface area. Drum Tight Containers is designing an open-top, square-based,…

A: Volume of a cuboid is lbh. Since it is mentioned that it is square-based so l=b. l2h=62.5 in3…

Q: Maximum-volume cylinder in a sphere Find the dimensions ofthe right circular cylinder of maximum…

A: We have to find the dimensions of the right circular cylinder of maximum volume that can be placed…

Q: 55. A cardboard box without a lid is to have a volume of 32,000 cm³. Find the dimensions that…

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Q: A box with an open top has vertical sides, a square bottom, and a volume of 32 cubic meters. If the…

A: Consider the given information about the box:

Q: 19. Minimizing surface area. Mendoza Soup Company is constructing an open-top, square-based,…

A: Given: Volume=32 ft3

Q: A rectangular solid with a square base has a surface area of 37.5 square centimeters. (Let w…

A: (a) From the given, the surface area of the rectangular solid with square base is 37.5 cm2. Let the…

Q: An open box is made from a square piece material with sides 3 feet by 3 feet by cutting equal…

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Q: 25) From a thin piece of cardboard 10 in. by 10 in., square corners are cut out so that the sides…

A: Given The size of the cardboard is 10 in by 10 in Let x be the length of the cut out portion that is…

Q: (a) Show that each of the rectangular solids given in figure has a surface area of 150 square…

A: "Since you have asked multiple questions we will solve the first question for you. If you want any…

Q: 21. Minimizing surface area. An oil drum of standard size has a volume of 200 gal, or 27 ft³. What…

A: Let the radius of the drum be rft and height be hft. As the volume of the drum is 27ft We get…

Q: A rectangular tank with a square base, an open top, and a volume of 10,976 ft is to be constructed…

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Q: 7. A closed box with square ends is to be constructed in such a way that its total surface area is…

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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: 4. A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The…

A: Volume of the cylinder , V=πR2h Volume of the hemisphere ,V=43πR3

Q: A rectangular tank with a square base, an open top, and a volume of 27,436 ft is to be constructed…

A: Given: - A rectangular tank with a square base, an open-top, and a volume of 27436ft3 is to be…

Q: A certain airline requires that rectangular packages carried on an airplane by passengers be such…

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Q: A closed cylindrical container has a surface area of 400cm². Determine the dimensions for maximum…

A: A function will have a maximum at a point where the value of the first derivative of the function…

Q: How do you answer the problem in the attached image?

A: It is given that the volume if the rectangular solid is 1000 cu in.

Q: A rectangular tank with a square base, an open top, and a volume of 2,916 ft° is to be constructed…

A: Here I am attaching image so that you understand each and every step.

Q: ctangular box is to contain 125 in³. Find the dimensions of the box for which the surface area is…

A: Given query is to find the  dimensions for minimum surface area.

Q: Find the minimum volume of a right circular cylinder that can be inscribed in a sphere having a…

A: We need to find the minimum volume of right circular cylinder that can be  inscribed in a sphere…

Q: A rectangular box, open at the top, is to contain 32 in³. Find the dimensions of the box for which…

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Q: 1. A box with a square base is to have an open top. The area of the material for making the box is…

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Q: This question is under the topic optimization and related rates

A: All the dimensions are in inches, surface area is in square inches and volume is in cubic inches.…

Q: A rectangular base box must be constructed, with a sheet of cardboard 40 cm wide and 50 cm long,…

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Q: A rectangular box has three of its faces on the coordinate planes and one vertex in the first octant…

A: Given,The box's volume is  V = xyz  but we know that   z = 4 − x2 − y2V = xyz    = xy ( 4 − x2 − y2…

Q: a) Find the maximal volume of the rectangular box whose three faces belong to the coordinate planes…

A: Given: x+y+z=3

Q: A rectangular box with an open top and one partition is to be constructed from 288 square inches of…

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Q: (a) Show that each of the rectangular solids given in figure has a surface area of 150 square…

A: Since, Our Aim is to show that :-(a) Each of the rectangular solids given in figure has a surface…

Q: A rectangular solid with a square base has a volume of 4,096 cubic inches. (Let w represent the…

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Q: A box with an open top has vertical sides, a square bottom, and a volume of 108 cubic meters. If the…

A: A box with an open top has vertical sides, a square bottom Let's assume length of box =x Since, base…

Q: You are making a rectangular box with a square base. Its volume must be 8 ft^3 . Find the dimensions…

A: A rectangular box with a square base. Its volume must be 8 ft3

Q: 1. An open-top box with a square base is made from a cardboard of area 75 cm². Find the maximum…

A: given area is 75cm2find the maximum volume of the box

Q: You are designing a glass candle holder.  It will be a rectangular prism with outer surface area 200…

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Q: A rectangular solid with a square base has a surface area of 121.5 square centimeters. (Let w…

A: Let w represent the width of the sides of the square base and h represent the height of the…

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

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Q: A rectangular box with an open top has a square bottom and a volume of 4 m³. Find the dimensions of…

A: Given that the volume of the rectangular box is 4 m3 and its bottom is a square.

Q: A rectangular box has a square base whose edges have length at least one centimeter, and its total…

A: We will use Calculus to maximize the volume with the given constraint of the total surface area. We…