A closed three dimensional box is to be constructed in such a way that its volume is 3000 cm³. It is also specified that the length of the base is 4 times the width of the base. Find the dimensions of the box that satisfies these conditions and has the minimum possible surface area.

Q: An open-top box is to be made from a 20 in by 30 in piece of cardboard by removing a square from…

A: Let each side of the square cut-off from each corner be x in. then the length of the base of the box…

Q: The volume of an open box with a square base is 4000 cm3. Find the dimensions of the box if the…

A: Given that volume =4000cm3 find the dimensions of the box that minimize the amount of material used…

Q: 4. An open-top box with a square bottom and rectangular sides is to have a volume of 256 cubic…

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Q: A solid steel cylinder is to be produced so that the sum of its height h and diameter 2r is to be at…

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Q: 3. Find the dimensions of a open topped box that maximizes the volume with the constraint that the…

A: We need to find dimension of an open box that maximizes the volume.

Q: A triangle has variable sides x, y, and z subject to the constraint such that the perimeter is fixed…

A: Given that , The sides of triangle are x,y and z and perimeter = 18 cm ⇒x+y+z=18  Find maximum…

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: A box with square bottom and no top is to contain 32 cubic inches Find the dimensions that will lead…

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Q: A rectangular sheet of metal having dimensions 20cm by 12cm has squares removed from each of the…

A: A rectangular sheet of metal having dimensions 20cm by 12cm has squares removed from each of the…

Q: A box with a square base and open top must have a volume of 62,500 cm3. Find the dimensions of the…

A: Let the length of the sides of the base= x cm Height = y cm

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Q: A closed rectangular box to contain 16 ft³ is to be made of three kinds of materials. The cost of…

A: Easy to handle two variables rather than three variables, so i substitute by a variables by other…

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

A: According to the question, we have a rectangular box and the sum of the lengths of its 12 edges is…

Q: A rectangular tank with a square base, an open top, and a volume of 5324 ft is to be constructed of…

A: Given: Rectangular tank with square base (open at the top) Volume is 5324 cubic feet. To find: The…

Q: Find the maximum and minimum volumes of a rectangular box whose surface area equals 10000 square cm…

A: We have to find out maximum and minimum volume

Q: Find the length L and width W (with W less than or equal to L) of the rectangle with area of 198…

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Q: A box with no top and a square base has to be designed so that its volume must 108 cm³. Find the…

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Q: A Box with a Square base and an open Top must have a volume of 500 cm'. Find the dimensions of the…

A: A box with a square base and an open top must have a volume of 500 cm. To find: The dimensions of…

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

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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…

A: Question is solved.

Q: A rectangular hole is to be cut in a wall for a vent. If the perimeter of the hole is 48 in. and the…

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

A:

Q: A rectangular tank with a square​ base, an open​ top, and a volume of 37,044 ft3 is to be…

A: Given,Volume of the rectangular tank = 37044 ft3

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: A piece of wire of length 1 meter is cut into two parts, one of which is bent into the shape of a…

A: A piece of wire of length 1 meter is cut into two parts , one of which is bent the shape of a circle…

Q: The base of an aquarium with given volume V is made of slate and the sides are made of glass. If the…

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Q: A box with an open top and square base is to be created with a surface area of 300 square inches.…

A: The box is open  And base is square  Let square sides l = b = x in And height  =h in

Q: Suppose that a pentagon is composed of a rectangle topped by an isosceles triangle. If the length of…

A: We have to find the maximum area.

Q: 1. Find the dimensions of a rectangular box with a square base and no top that has a volume of 100…

A: Solve By minimizing surface area

Q: A poster is to contain 300 cm2 of printed matter with margins of 10 cm at the the top and bottom and…

A: We have, A poster is to contain 300 cm2 of printed matter with margins of 10 cm at the the top and…

Q: A rectangular tank with a square base, an open top, and a volume of 8788 ft 3 is to be constructed…

A: A rectangular tank has square base Let x be the base of the tank  and y be the height  x is the…

Q: A box with a square base and open top must have a volume of 32000 cm³. Find the dimensions of the…

A: To find the dimensions of the box that minimize the amount of material used to construct it.

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: With only 600 m2 of materials, a closed cylindrical tank is to be made. What should be the height of…

A: Let's find.

Q: Find the dimensions that will give the minimum surface area for a crate that has a volume of 13.5…

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Q: 2) An open box constructed from a tin sheet has a square base and a volume of 216 in cubed. Find the…

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Q: A company that manufactures dog food wishes to pack the food in closed cylindrical tins. What should…

A: Use application of derivative concept. volume of cylinder and total surface area of cylinder…

Q: a rectangular tank that is 864 ft cubed with a square base and open top is to be constructed of…

A: Let the measure of side of square base of tank  is x ft and height of tank is y ft and volume of…

Q: Find the maximum and minimum volumes of a rectangular box whose surface area equals 8000 square cm…

A: Let the three sides or edges of the rectangular box be a,b and c in cm. Surface area of the box will…

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

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Q: 4. Four identical bricks are stacked up on top of each other. Each has a length of a and a mass of…

A:

Q: 1. A closed box, with a rectangular base, whose length is twice its width, is to have a surface of…

A: Topic.- application of derivatives Given: Length is twice the width and the total surface area is…

Q: A printed page is to contain 60 cm2 of printed material (not including the margins) with margins (on…

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Q: An open topped box is to be made from a rectangular piece of metal 18cm x 48 cm by cutting off…

A:

Q: A rectangular tank with a square base, an open top, and a volume of 16,384 ft° is to be constructed…

A: Given : Volume of rectangular is given 16384 ft3  Now we find surface Area and 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…

Q: Find the dimensions of a open topped box that maximizes the volume with the constraint that the…

A: We will use Lagranges multiplier method to find dimension of the box .

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…