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

Q: Use calculus to find the volume of a tetrahedron (pyramid with four triangular faces), all of whose…

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Q: A closed, rectangular-faced box with a square base is to be constructed using only 16 m? of…

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Q: An open box is to be made out of a 10-inch by 20-inch piece of cardboard by cutting out squares of…

A: Draw the diagram for the given problem for the given conditions and then find the volume

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: A box with a square base and open top must have a volume of 32m3. Find the dimensions of the boxthat…

A: Given,  V=32 m3                                      ..........................(1) The amount of…

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

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Q: Find the volume of the tetrahedron with the given vertices. (1, 0, 0), (0, 2, 0), (0, 0, 1), (1, 2,…

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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: A box with a square base with side length b and height h and with an open top must have a volume of…

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Q: Find the volume of the tetrahedron with the given vertices.(1, 1, 1), (0, 0, 0), (2, 1, −1), (−1, 1,…

A: The vertices of tetrahedron are A(1, 1, 1), O(0, 0, 0), B(2, 1, −1),C (−1, 1, 2) Then,

Q: An open box is to be made out of a 12-inch by 14-inch piece of cardboard by cutting out squares of…

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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: what are the dimensions of the right hexagonal prism of minimum surface whose volume is 36 cubic…

A: This is a problem of optimization.

Q: A shipping company handles rectangular boxes provided the sum of the length, width, and height of…

A: Let the dims be x, y and z then volume V=xyz           -----------(1) and the restriction we have…

Q: Find the dimensions of a box with largest volume whose surface area is 100 cm?. Lagrange multipliers

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Q: Which set of dimensions belongs to a right rectangular prism with a volume of 440 cm3?

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Q: Find the volume and the surface area of a “closed boOx' that has dimensions of 15 cm, 20 cm, and…

A: Given that: The dimensions of a " closed box" are 15 cm , 20 cm and 0.25m. 1m = 100 cm

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

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Q: 6. Find the minimum surface area of a box that holds 2 cubic meters.

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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: Find the volume of the tetrahedron with the given vertices.(1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1,…

A: We have given the vertices of tetrahedron; (1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 1) Since volume…

Q: Find the volume enclosed by the cy linder (x-1) ty²=1 and the sphere x² +y²7z²=L4.

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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: In constructing an open rectangular box from 192 ft? of material, what dimensions will result in a…

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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 volume of a right triangular prism whose altitude is 3m and a right triangular base whose…

A: Given, A right triangular prism whose altitude is 3m and a right triangular base whose legs are 1m…

Q: What is the maximum volume of a cone that would fit this box?

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Q: Consider an open top rectangular box with a square base. Find the dimensions of the box for which…

A: S

Q: Use calculus to find the volume of a tetrahedron​ (pyramid with four triangular​ faces), all of…

A: If a solid is from x =a to x= b and the area of its base is A then the volume of the solid is given…

Q: Given that a regular polyhedron of n faces is inscribed in a sphere of radius length 6 in., find the…

A: Given:              A regular polyhedron of n faces is inscribed in a sphere of radius length 6 in.

Q: Find the volume of the maximum volume square prism that can be placed inside a sphere with a radius…

A: Given The radius of sphere 3√2. We find the diameter of sphere

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: Find the volume of the tetrahedron with the given vertices.(0, 0, 0), (0, 2, 0), (3, 0, 0), (1, 1,…

A: The given vertices of a tetrahedron are (0,0,0), (0,2,0), (3,0,0) ,(1,1,4)

Q: A closed, rectangular-faced box with a square base is to be constructed using only 16 m² of…

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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: 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

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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: An open rectangular box has an area of 441 cm2. If its length must be 3 times its width, find its…

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Q: A box, used to package men's shirts, is in the shape of a square-based prism and its to have a…

A: Given Data: The volume of the square-based prism is: V=8400 cm3 The equation of surface area is:…

Q: Find the dimensions of the box with square base with: (a) Volume 12 and the minimal surface area.…

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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: What is the largest possible volume of a rectangular box whose diagonal has length L?

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Q: if an open box has a square base and a volume of 256 in^3 and is constructed from a tin sheet.  Find…

A: Given

Q: Find the rectangular box of maximum volume if the sum of the lengths of the edges (x + y + z) is 324…

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Q: A rectangular box with no top is to have a surface area of 16 m2. Find the dimensions (in m) that…

A: Use derivative test for calculating the maximum volume of a rectangular box. Assume that base of box…

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: Determine the dimensions of the rectangle of largest area that can be inscribed in a semicircle of…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its…

A: To find: Dimension of a rectangular box. Given: Volume of the box is maximum and sum of edges of box…