\ Use optimization to find the maximum volume of a box with one corner at the origin and the opposite corner on the plane r+y+z = 1. 3.

Q: Find the volume of the maximum volume rectangular prism that can be drawn inside the ellipsoid so…

A: According to the given information, it is required to find the volume of the maximum volume…

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

A: Given, A sphere of radius 15 cm  We have to find the height of the right circular cylinder of…

Q: Find the dimensions of the rectangular box of maximum volume that has three of its faces in the…

A: Let say that(a,b,c) is point in plane 4x+3y+z=12 and it is one vertex of requested rectanglar box.…

Q: A cylindrical container with a circular base and open top must have a volume of 1000 m³. Find the…

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Q: Determine the dimensions of the right circular cylinder of maximum lateral surface area that can be…

A: Maximum lateral surface area will occur at critical point  So put ds/d(theta) = 0 Find theta

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

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Q: Find the dimensions and volume of the right circular cylinder of maximum volume inscribed in a…

A: Let r be the radius of the cylinder and h be the height of the cylinderR is the radius of the sphere…

Q: We want to construct a box with a square base that has a volume of 100 cm^3 . Assuming that all the…

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Q: You want to design a box with a square base such that the sum of its length, width and height does…

A: We have given that the dimension of the box is not exceed 51 .

Q: A covered box is to be made from a rectangular sheet of cardboard measuring 35 inches by 56 inches.…

A: Solution: According to the question the diagram will be

Q: You want to design a box with a square base such that the sum of its length, width and height does…

A:

Q: ind the center of mass for a thin plate covering the region bounded by the parabola y=25-x^2 and…

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Q: An open top box with a square base is to be constructed so that it will have a volume of 2 m’. What…

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Q: A solid right cylindrical cement block of volume 97 ft³ is to be made, and then painted except for…

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Q: A silo (base not included) is to be constructed in the form of a cylinder surmounted by a…

A: Given: The cost of the surface area of the hemisphere is twice the cost of the surface area of the…

Q: Find the dimensions and volume of the right circular cylinder of maximum volume inscribed in a…

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Q: The surface area of ​​a cylindrical box with an open top is 27π ^ 2. Dimension the cylinder so that…

A: We have to find the expression for the volume first.

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

A: Draw the diagram roughly.

Q: Find the dimensions of a right circular cylinder of maximum volume which can be inscribed in a…

A: NOTE: Refresh your page if you can't see any equations. . the radius of the sphere is R=12 the…

Q: Find the dimensions (both radius and height) of a soup can with a volume of 432 cm³ that minimize…

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

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Q: How do I find the dimensions of a right circular cylinder of greatest volume that can be inscribed…

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Q: A rain gutter is made from sheets of aluminum that are 12 inches wide by turning up the edges to…

A: Given that, The three sides of the rain gutter is add up to 12 inches              2x+y=12⇒y=12-2x…

Q: Waste Management Company want to construct a dumpster in the shape of a rectangular solid with no…

A: Consider w as the width of the rectangular solid.Then, the length is 3w.Volume of the solid is 18…

Q: A cylinder is inscribed in a right circular cone of height 2.5 and radius (at the base) equal to 4.…

A:

Q: A company plans to manufacture a rectangular bin with a square base, an open top, and a volume of…

A: According to the given information:Let length of the rectangular bin be ‘x’ cmBreadth of rectangular…

Q: A box used for shipping goods is required to have the sum of its girth (perimeter of its…

A: The given figure is:

Q: 3. Explain how we know that it is possible to cut a surface with continuous boundaries in exactly…

A: We should mathematically establish the possibility of cutting a surface with continuous boundaries…

Q: A cylinder is inscribed in a sphere with radius 4. Find the height h of the cylinder with the…

A: given radius of sphere  R = 4. r is the radius of cylinder inscribed. and h be the height of…

Q: A cylindrical kite frame is to be constructed from a 4 metre length of bendable  steel rod. The…

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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: The total amount of a cylinder inserted into a hemisphere of radius 1 unit Finds the maximum value…

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Q: Find the most economical shape (i.e. minimum surface area because it costs less) for a cylindrical…

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Q: A rectangle with a fixed perimeter of 64 units is rotated about one of its sides,  thus sweeping oit…

A: To Determine: What is the maximum volume of that  cylinder. Given:  A rectangle with a fixed…

Q: A silo (base not included) is to be constructed in the form of a cylinder surmounted by a…

A: Given that the cost of construction per square unit is twice as great as for the hemisphere as it is…

Q: Consider a rectangular box B that has a bottom and sides but no top and has minimal surface area…

A: Given information: V=64 m3

Q: Two factories are located at the coordinates (−x, 0) and (x, 0), and their power supply is at (0,…

A: To Determine: Find y such that the total length of power line from the power supply to the factories…

Q: A candy box is made from a piece of cardboard that measures 35 by 19 inches. Squares of equal size…

A: Consider the length of the cardboard is 35 in and width of the cardboard is 19 in Suppose length of…

Q: Find the volume of the region above the triangle with vertices (1,0), (0,1) and (3,1), below the…

A: Given Data: fx,y=x2y The vertices of the triangles are (1,0), (0,1) and (3,1).

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

A: Find the radius of the cylinder that produces the minimum surface area

Q: A box with square base and open top has a volume of 1000 m³. Find the dimensions of the box which…

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

Q: here having a radius of 3cm. is cut in the shape of a circular cone of maximum volume. is the…

A: Topic:- application of derivatives

Q: An oil storage tank can be described as the volume generated by revolving the area bounded by…

A: Given: y=49+x214, x=0, y=0, x=2 To determine: The volume of the tank generated by revolving the area…

Q: Waste Management Company wants to construct a dumpster in the shape of a rectangular solid with no…

A: We need to find dimension.

Q: a rectangular solid with a square base has a surface area of 450 square centimeters. find the…

A: Let x cm be the side of square base and y cm be the height of rectangular solid. Then surface area…

Q: Right circular cones of height h and radius r are attached to each end of a right circular cylinder…

A: Let Vcr be the volume of the cone and Vc be the volume of the cylinder. So, Vcr=πr2h and Vc=13πr2h.

Q: A cylindrical diet coke can is being made out of 54π in2 of material. What dimensions maximize the…

A: Given Material used in cylindrical diet coke= 54π in2 Want to maximize the volume of A cylindrical…

Q: You want to design a box with a square base such that the sum of its length, width and height does…

A: Given query is to find the maximum possible volume for the box with the given data.