Find the dimensions of the rectangular box of maximum volume that can be inscribed inside the sphere x2 + y2 + z2 = 4.

Q: An open box with a square base is to have a volume of 12ft^3. find the box dimensions that minimize…

A: The volume of a rectangular prism(cuboid) = l×b×h Let y = measurement of each side of the base, h =…

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: Find the volume of the largest rectangular box in the first octant with three faces in the…

A: The given equation of plane is : x+2y+3z=6 x=6-2y-3z                   …(1) Volume of a rectangular…

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

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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: Find the dimensions of the right circular cone of minimum volume V that can be circumscribed about a…

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Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

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Q: Find the dimensions of the rectangular box of maximum volume with faces parallel to the coordinate…

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Q: 4. Find the volume of the wedge cut from the first octant by the cylinder z = 12 - 3y2, and the…

A: We have to find volume.

Q: Show that a closed right circular cylinder of given surface has maximum volume if its height equals…

A: Let, the surface area be S, radius be r, height be h and volume be V. The total surface area be…

Q: Find the dimensions of a cylindrical can with a bottom but no top of volume 4 m3 that uses the least…

A: To Find: Dimension of a cylindrical can with a bottom but no top of volume 4 m3that uses the least…

Q: 3. What are the dimensions of the closed cylindrical can that has surface area 280 square…

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Q: A box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the…

A: To find the dimensions that minimize area

Q: You are to construct an open rectangular box from 12 ft2 of mate-rial. What dimensions will result…

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Q: A thin plate of constant density k, bounded by the parabola y=3x² and the line y=3 has a mass 4k.…

A: If mass of a region R bounded between y=f(x) and y=g(x) from x=a  to x=b  Then there two moments,…

Q: A rectangle with perimetee 18 cm is rotated about one of its sides forming a a right circular…

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Q: Find the dimensions (radius r and height h) of the cone of maximum volume which can be inscribed in…

A: According to our company policy, I am supposed to answer only one question at a time so for the rest…

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: Find the volume of the largest rectangular box in the first octant with three faces in the…

A: We have to find the volume of the largest rectangular box in the first octant with three faces in…

Q: we have 27ft squared of material to build a box of maximum volume with a square base and no top.…

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Q: A jewelry box with a square base is to be built with copper platedsides, nickel plated bottom and…

A: Given that Volume of the  box is 40 cm3 Base of the box is square. Let  length =width=x Height=y…

Q: A rectangular storage container with a square base and an open top is to have a fixed volume of…

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Q: A box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the…

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

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Q: What are the dimensions of an open-top right circular cylindrical can that will hold a volume of 512…

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Q: find the dimension of a cylinder that can be inscribed in a given sphere if it's convex surface area…

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Q: A box with a square base and open top must have a volume of 32,000 cm3. Find the dimensions of the…

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

A: Solved below

Q: Find the surface area of the portion of the half ball with radius a which cuts off by the cylinder…

A: The equation of a ball with radius a is x2+y2+z2=a2. The surface area of the function z=fx,y over…

Q: Find the dimensions of a cylinder of volume 1 m 3of minimal costif the top and bottom are made of…

A: Given: Find the dimensions of a cylinder of volume 1 m 3of minimal cost if the top and bottom are…

Q: Find the maximum volume of a cylindrical can such that the sum ofits height and its circumference is…

A: Let r denotes radius       h denotes height Then       volume of cylinder (V) = πr2h Restriction is…

Q: A cylinder with no top is to have a volume of 100π cubic centimeters. Find the minimum possible…

A: To find the minimum possible surface area of the given type of cylinder.

Q: To calculate: The dimension of the rectangular solid with a square base that yields the minimum…

A: The rectangular solid has a square base. Let the dimensions of the rectangular solid be x, x and y.…

Q: A cylindrical can has a volume of 1024r cm. What dimensions yield the minimum surface area?

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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: A box with a square base and open top must have a volume of 4,000 cm³. Find the dimensions of the…

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Q: Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its…

A: Follow the procedure given below.

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: Show that the rectangular box of maximum volume that can be inscribed in the sphere x^2 + y^2 + z^2…

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Q: A company is constructing an open-top square-based, retangular metal tank that will have a volume of…

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Q: The volume of a box without a top is 36 m3, where the length is twice of width. Find the dimensions…

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Q: Use Lagrange multipliers to find the dimensions of a box with volume 1000 cm3 that has minimal…

A: the surface area of the box is  S=2xy+2yz+2xz................(1) the volume of the box is given by…

Q: A box with a volume of 512cm3 is to be constructed. The sides of the box cost 2 cents per cm2, and…

A: Given the volume of the box is

Q: A box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the…

A: Consider a box with square base and open Top and have a volume of 4000 cubic centimeters. Let the…

Q: A box with a square base and open top must have a volume of 32,000cm3 . Find the dimensions of the…

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Q: A box with a square base and open top must have a volume of 13,500 cm3. Find the dimensions of the…

A: To find the dimensions

Q: A rectangular tank that is 1372 ft° with a square base and open top is to be constructed of sheet…

A: The tank with minimum weight is the one with minimum surface area. Since the base is square, its…