Find the most economical proportions for a covered box of fixed volume whose base is a rectangle with one side three times as long as the other.

Q: A gutter with trapezoidal cross section is to be made from a long sheet of tin that is 18 inches…

A: Given that , Total length of the sheet = 18 inches find width across the top will give the greatest…

Q: if 900 square centimeters of material is available to make a box with a square base and an open top,…

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Q: 2. Find how fast the volume, surface area and diagonal of a cube as the length of the edge

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Q: An open rectangular box with square ends to hold 6400 cu ft, is to be built at a cost of $75 per sq…

A: Given that, An open rectangular box with square ends to hold 6400 cu ft. Thus, V= x2 y. 6400 = x2y…

Q: An open rectangular box with square ends to hold 6400 cu ft., is to be built at a cost of $0.75 per…

A: The rectangular box is square at base and opened at top.So we will not be involving top of the box…

Q: A rectangular piece of metal is 30 in longer than it is wide. squares with sides 6 in. long are cut…

A: Consider the provided question,Let width of the rectangular piece of metal = x in.Length = (x + 30)…

Q: A delivery company wants to come up with a package box that has a square base and a volume of 40…

A: Given, Let's assume the side of the square base = a Height of the box  = h Volume = area of  base *…

Q: An open-top box is to be made by cutting small congruent squares from the corners of a…

A: Let the length of the side of the square is x in So the height of the box= x in  Length = (12-2x) in…

Q: Determine the dimensions of a rectangular box, open at the top, having a volume of 32 ft³, and…

A: Determine the dimensions of a rectangular box, open at the top, having a volume of 32 ft³, and…

Q: The base of the pyramid is 72 cm, and the length of TP = 15 cm. The volume of the pyramid is..

A: Let B be a base B=72cmLet h be a length of TP h=15cmVolume of pyramid =13Bh=13×72×15=360 cm3

Q: Find the minimum amount of tin sheet in square inches that can be made into a closed cylinder having…

A: Find the minimum amount of tin sheet in square inches that can be made into a closed cylinder having…

Q: If a spherical tank 4 m in diameter can be filled with a liquid for $250, find the cost to fill a…

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Q: Find the largest volume of a rectangular box with no top made by cutting little squares out of the…

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Q: A hall is 1 m long and 2 m broad. If the sum of the areas of the floor and the the ceiling is equal…

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Q: A lont strip of sheet metal 12 inches wide is to be made into a small trough by turning up two sides…

A: Let x be the sides and B is the base. Perimeter is 12. The cross section of the area is given by…

Q: Find the volume of a cone with a base circumference of 19π cm and a height 6 cm less than twice the…

A: base of the cone is circle

Q: A steel storage tank for propane gas is to be constructed in the shape of a right circular cylinder…

A: Given, A steel storage tank for propane tank gas is to be constructed in the shape of a right…

Q: Find the volume of the largest box with no top that can be made from a piece of cardboard 30 inches…

A: Given that a box with no top has to be made from a piece of square cardboard of side  30 inches by…

Q: a rectange is 4 inches longer than it is wide. numerically its area exceeds its perimeter by 17.…

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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 rectangular plot of land is to be seeded with grass.  If the plot is 18 m by 20 m and a 1kg bag of…

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Q: The owner of the Rancho Grande has 2,980 yds of fencing with which to enclose a rectangular piece of…

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Q: If 900 square centimeters of material is available to make a box with a square base and an open top,…

A: Surface of a box which is open from the top.It is the the sum of the a2 and 4 rectangles . Let base…

Q: What are the dimensions for the cheapest possible rectangular box with a volume of 56 cm if the…

A: Consider the provided question, Let length of the box = l cm Width of the box = w cm And, height of…

Q: Find the dimensions of a rectangle with perimeter 80 m whose area is as large as possible.

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Q: Find the cost of pouring a square concrete slab of uniform thickness with sides of 45 ft if the cost…

A: Side of square = 45 ft Area of square = (side)2 = 452 = 2025 sq ft. Cost of 1 square ft = $5.25…

Q: In a hollow cylinder, the sum of the external and internal radii is 14 cm and the width is 4 cm. If…

A: Given that, the sum of the external and internal radii is 14 cm and the width is 4 cm. The height of…

Q: A piece of cardboard 4 ft by 4 ft will be made into an open topped box by cutting squares out of…

A: Summary... Cut should be of size  2/3 ft

Q: If a rectangular garden is 6 feet long and 4 feet wide and there are 10 vegetables planted; what is…

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Q: if the mass of a cube were 48G and it’s volume 24CM3 what would be its density

A: Given, mass=48g Volume=24cm3

Q: If 1200 cm² of material is available to make a box with a square base and an open top, hnd the…

A: Total area is given so first let the base length is a and height is h .. then make the relation of…

Q: The U.S Post Office will accept a box for shipping only if the sum of the length and girth (distance…

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Q: A rectangula plot of land is to be seeded with grass. If the plot is 16 m by 12 m and a 1kg bag of…

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Q: Suppose you wanted a flat that would hold 9,000 cubic centimeters of strawberries. What would be the…

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Q: If 10,800 cm2 of material is available to make a box with a square base and an open top, find the…

A:

Q: determine the dimensions of a rectangular tank open at top having the volume of 108 cm^3 and…

A: Finding the dimensions of the box using the given conditions

Q: If 30,000 cm2 of material is available to make a box with a square base and an open top, find the…

A:

Q: An aquarium with rectangular sides and bottom (and no top) is to hold 5 gal. Find its proportions so…

A: Let the dimensions of a rectangular aquarium is Length =l Width=w Height=h Now, The volume is,…

Q: If 1200cm^2 of material is used to make a box with square base and open top, find the largest…

A: Box is the open top with the square base, let x be its length and width, and h be its height. Then…

Q: An open box is to be made from a square piece of married by cutting  4 cm squares from each corner…

A: Given, The volume of the finished box is 324 cm3.The side of the cutting squares is 4 cm.To find the…

Q: If 10,800 cm2 of material is available to make a box with a square base and an open-top, find the…

A: Answer is mentioned below

Q: If 1400 square centimeters of material is available to make a box with a square base and an open…

A: Explained below

Q: A dog trainer has 58ft of fencing with which to create a rectangular work area for dogs. If the…

A: Given that a dog trainer has 58 ft of fencing with which to create a rectangular work area for dogs.…

Q: An open rectangular box with square ends is to be built to hold 392 ft3 at a cost of Php 75/ft2 for…

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Q: Multivariable optimization question

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Q: A machine produces open boxes using square sheets of metal. The machine cuts equal-sized squares…

A: Definition used -                The volume of box  = Area of base x height…

Q: Your team has contracted to design and build a 500 ft³, square-based, open-top, rectangular steal…

A: surface area of rectangular field = A=4×length×height+length×breadth. Volume of rectangular field:…

Q: A cone has a volume that is 350 cubic meters. What is the volume of a similar cone that is twice as…

A: Given, Volume of 1st cone = 350 cubic meters To find the volume of a similar cone that is twice as…

Q: If 1200cm2 of material is available to make a box with a square base and an open top, find the…

A: We have considered each side of the square base is x cm and the height of the box is h cm.