Find the rectangular parallelepiped of fixed total edge length with maximal surface area.

Q: Find the dimensions of the box with square base, surface area 20, and maximal volume.

A: A box with square base has surface area 20we have to find its dimension and maximum volume.

Q: A cube of edge 4 in is cut by a plane containing two diagonally opposite edges of the cube. Find the…

A: Given that each edge of the cube is 4 inches long. The cube is cut by a plane containing 2…

Q: Show that a rectangular box of given volume and minimum surface area is a cube.

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

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Q: 24. Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1,…

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Q: A farmer uses 2000 feet of fence to enclose a rectangular region and also to subdivide the region…

A: Let the width of the fence be:  w Let the length of the fence be:  l

Q: Show that among all rectangles with a given perimeter, the square is the one with the maximum area.

A: A rectangle is a quadrilateral whose opposite sides are equal and parallel to each other. The…

Q: If the farmer has 246 feet of fencing, what are the dimensions of the region which enclose the…

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Q: Determine the dimensions of a rectangular box with a volume of 1 ft ^ 3 that has a minimum surface…

A: Given a rectangular box with volume 1 ft^3

Q: What is the largest possible area such a region can have if its perimeter is to be 20 units?

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Q: Show that the rectangular parallelepiped with fixed surface area and maximum volume is a cube.

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Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS: P(-2,1,0), Q(2,3,2),…

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Q: Of all boxes with square base and a volume of 512 cm, which one has the minimum surface area? (Give…

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Q: A landowner wishes to use 2 miles of fencing to enclose a rectangular region of maximum area. 1.…

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Q: A closed rectangular box has volume 26cm^3. What are the lengths of the edges giving the minimum…

A: Given a rectangular box which has volume 26 cm^3.

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: What is the maximum total area of such a corral?

A: Let the length of rectangular corral = LBreadth of rectangular corral = BPerimeter of rectangular…

Q: The maximum possible volume of a rectangular box with the sum of its twelve edges 60 cm is

A: Given 12 edges sum is 60, let C=60So, 4x+4y+4z=CV=xyz    =xy(14C-x-y)    =14Cxy-x2y-xy2 for x>0,…

Q: Find the volume of the parallelepiped defined by the inequalities 0≤2x−3y+z≤5,1≤x+2y≤4,−3≤x−z≤6.

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Q: West Coast Customs is constructing a closed-top, square-based, rect- angular subwoofer box that will…

A: Here we use application of derivatives to find the minimum surface area and find it's dimensions.

Q: Find the dimensions of a rectangle of maximum area inscribed in a circle of radius 4. (Must show…

A: Let ABCD be the rectangle inscribed in the circle of radius 4. AC and BD are the diameters of length…

Q: Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 cm2 and whose…

A: Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 cm2 and whose…

Q: A closed rectangular box has volume 20 cm³. What are the lengths of the edges giving the minimum…

A: Solution is given below:

Q: a

A:

Q: Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the…

A: Let 2x, 2y, 2z be the dimensions of rectangular box. Then Let

Q: what is the minimum perimeter that a rectangle with an area of 32 ft2 can have?

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Q: A farmer wants to enclose a rectangular field with area 1,000 square meters by fencing it into four…

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Q: 8.Show that the rectangular box of maximum volume with a given surface area is a cube

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Q: Find the volume of the parallelepiped with adjacent edges PQ, where P (1,1, 1), Q (2,0,3,), R =…

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Q: Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1, 0,…

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Q: Find the dimensions of the rectangle of greatest area that can be inscribed in a circle of radius a.

A: Let x and y be the length and width of the rectangle inscribe in a circle of radius a. Then the…

Q: Find the maximum volume of a rectangular box whose surface area is 1600 cm? and whose total edge…

A: By using lagrange multiplier

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(-2, 1, 0), Q(3, 4, 3),…

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Q: A closed rectangular box has volume 22 cm3. What are the lengths of the edges giving the minimum…

A: Minimization problem

Q: A rectangular building covering 7000 m² is to be built on a rectangular lot as shown below. If the…

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Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS, where P(3, 0, 1), Q(2, 3,…

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Q: Find the volume of the parallelopiped with adjacent edges PQ, PR, PS where P(-2, -1, -3), Q(0, 2,…

A: The given points P-2,-1,-3, Q0,2,0, R-3,-2,-4, S4,-3,-1

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

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Q: Find the dimensions of a rectangle with area 100 m? whose perimeter is as small as possible? Find…

A: to find:- dimensions of the rectangle. minimum perimeter.

Q: What is the least number of lateral edges of a prism?

A: Given that: A prism.

Q: If the farmer has 648 feet of fencing, what are the dimensions of the region which enclose the…

A: x = length of the rectangle y = width of the rectangle fencing =648 ft hence 2x + 3y = 648 x…

Q: should the box have in order to minimize the surface area?

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Q: Of all rectangles with a perimeter of lo meters, which one has the maximum area? (GIve both the…

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Q: Is the rectangle of fixed area whose perimeter is a minimum a square?

A: Given Area of a rectangle =  square units-----(1)   Let length of the rectangle be feet and the…

Q: Of all rectangles with area 64, which one has the minimum perimeter?

A: It is required to find the dimensions of rectangle having area 64 units which will have a minimum…

Q: 4. West Coast Customs is constructing and open-top, square-based, rect- angular subwoofer box that…

A: West Coast Customs is constructing and open-top, square-based.rectangular subwoofer box that will…